assignment
find the total value of the investment after the time given.
1) $420 at 3% compounded annually for 4 years
2) $215 at 6% compounded annually for 2 years
3) $5,000 at 6% compounded annually for 2 years
4) $65 at 1% compounded annually for 9 years
5) $15,000 at 2% compounded annually for 5 years
6) $415 at 15% compounded annually for 4 years
7) $19,200 at 2% compounded annually for 9 years
8) $235 at 11% compounded annually for 2 years
9) $37,600 at 4% compounded annually for 2 years
10) $38,600 at 15% compounded annually for 3 years
11) $30 at 14% compounded annually for 5 years
12) $42,200 at 2% compounded annually for 2 years
13) $410 at 4% compounded annually for 2 years
14) $110 at 2% compounded annually for 9 years
15) $90 at 4% compounded annually for 2 years
16) $34,300 at 2% compounded annually for 7 years
17) $29,800 at 4% compounded annually for 2 years
18) $35,900 at 7% compounded annually for 4 years
19) $46,600 at 16% compounded annually for 2 years
20) $11,700 at 14% compounded annually for 4 years

Question

Accepted Answer

Let's solve the first problem (1) as an example, and you can follow the same method for the others. The formula for compound interest is $A = P(1 + r)^t$, where:
- $A$ is the amount of money accumulated after $n$ years, including interest.
- $P$ is the principal amount (the initial amount of money).
- $r$ is the annual interest rate (decimal).
- $t$ is the time the money is invested for in years.

### Problem 1: $420 at 3% compounded annually for 4 years
# Explanation:
## Step 1: Identify the values
$P = 420$, $r = 3\% = 0.03$, $t = 4$

## Step 2: Apply the compound interest formula
$A = 420(1 + 0.03)^4$

First, calculate $(1 + 0.03)^4$:
$(1.03)^4 \approx 1.12550881$

Then, multiply by the principal:
$A = 420 	imes 1.12550881 \approx 472.71$

# Answer:
The total value of the investment is approximately $\$472.71$.

### Problem 2: $215 at 6% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 215$, $r = 6\% = 0.06$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 215(1 + 0.06)^2$

First, calculate $(1 + 0.06)^2$:
$(1.06)^2 = 1.1236$

Then, multiply by the principal:
$A = 215 	imes 1.1236 = 241.574$

# Answer:
The total value of the investment is approximately $\$241.57$.

### Problem 3: $5,000 at 6% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 5000$, $r = 6\% = 0.06$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 5000(1 + 0.06)^2$

First, calculate $(1 + 0.06)^2$:
$(1.06)^2 = 1.1236$

Then, multiply by the principal:
$A = 5000 	imes 1.1236 = 5618$

# Answer:
The total value of the investment is $\$5618$.

### Problem 4: $65 at 1% compounded annually for 9 years
# Explanation:
## Step 1: Identify the values
$P = 65$, $r = 1\% = 0.01$, $t = 9$

## Step 2: Apply the compound interest formula
$A = 65(1 + 0.01)^9$

First, calculate $(1 + 0.01)^9$:
$(1.01)^9 \approx 1.09368527$

Then, multiply by the principal:
$A = 65 	imes 1.09368527 \approx 71.09$

# Answer:
The total value of the investment is approximately $\$71.09$.

### Problem 5: $15,000 at 2% compounded annually for 5 years
# Explanation:
## Step 1: Identify the values
$P = 15000$, $r = 2\% = 0.02$, $t = 5$

## Step 2: Apply the compound interest formula
$A = 15000(1 + 0.02)^5$

First, calculate $(1 + 0.02)^5$:
$(1.02)^5 \approx 1.1040808032$

Then, multiply by the principal:
$A = 15000 	imes 1.1040808032 \approx 16561.21$

# Answer:
The total value of the investment is approximately $\$16561.21$.

### Problem 6: $415 at 15% compounded annually for 4 years
# Explanation:
## Step 1: Identify the values
$P = 415$, $r = 15\% = 0.15$, $t = 4$

## Step 2: Apply the compound interest formula
$A = 415(1 + 0.15)^4$

First, calculate $(1 + 0.15)^4$:
$(1.15)^4 = 1.74900625$

Then, multiply by the principal:
$A = 415 	imes 1.74900625 \approx 725.84$

# Answer:
The total value of the investment is approximately $\$725.84$.

### Problem 7: $19,200 at 2% compounded annually for 9 years
# Explanation:
## Step 1: Identify the values
$P = 19200$, $r = 2\% = 0.02$, $t = 9$

## Step 2: Apply the compound interest formula
$A = 19200(1 + 0.02)^9$

First, calculate $(1 + 0.02)^9$:
$(1.02)^9 \approx 1.19509303$

Then, multiply by the principal:
$A = 19200 	imes 1.19509303 \approx 22945.79$

# Answer:
The total value of the investment is approximately $\$22945.79$.

### Problem 8: $235 at 11% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 235$, $r = 11\% = 0.11$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 235(1 + 0.11)^2$

First, calculate $(1 + 0.11)^2$:
$(1.11)^2 = 1.2321$

Then, multiply by the principal:
$A = 235 	imes 1.2321 = 290.5435$

# Answer:
The total value of the investment is approximately $\$290.54$.

### Problem 9: $37,600 at 4% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 37600$, $r = 4\% = 0.04$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 37600(1 + 0.04)^2$

First, calculate $(1 + 0.04)^2$:
$(1.04)^2 = 1.0816$

Then, multiply by the principal:
$A = 37600 	imes 1.0816 = 40668.16$

# Answer:
The total value of the investment is $\$40668.16$.

### Problem 10: $38,600 at 15% compounded annually for 3 years
# Explanation:
## Step 1: Identify the values
$P = 38600$, $r = 15\% = 0.15$, $t = 3$

## Step 2: Apply the compound interest formula
$A = 38600(1 + 0.15)^3$

First, calculate $(1 + 0.15)^3$:
$(1.15)^3 = 1.520875$

Then, multiply by the principal:
$A = 38600 	imes 1.520875 = 58705.775$

# Answer:
The total value of the investment is approximately $\$58705.78$.

### Problem 11: $30 at 14% compounded annually for 5 years
# Explanation:
## Step 1: Identify the values
$P = 30$, $r = 14\% = 0.14$, $t = 5$

## Step 2: Apply the compound interest formula
$A = 30(1 + 0.14)^5$

First, calculate $(1 + 0.14)^5$:
$(1.14)^5 \approx 1.92541464$

Then, multiply by the principal:
$A = 30 	imes 1.92541464 \approx 57.76$

# Answer:
The total value of the investment is approximately $\$57.76$.

### Problem 12: $42,200 at 2% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 42200$, $r = 2\% = 0.02$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 42200(1 + 0.02)^2$

First, calculate $(1 + 0.02)^2$:
$(1.02)^2 = 1.0404$

Then, multiply by the principal:
$A = 42200 	imes 1.0404 = 43904.88$

# Answer:
The total value of the investment is $\$43904.88$.

### Problem 13: $410 at 4% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 410$, $r = 4\% = 0.04$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 410(1 + 0.04)^2$

First, calculate $(1 + 0.04)^2$:
$(1.04)^2 = 1.0816$

Then, multiply by the principal:
$A = 410 	imes 1.0816 = 443.456$

# Answer:
The total value of the investment is approximately $\$443.46$.

### Problem 14: $110 at 2% compounded annually for 9 years
# Explanation:
## Step 1: Identify the values
$P = 110$, $r = 2\% = 0.02$, $t = 9$

## Step 2: Apply the compound interest formula
$A = 110(1 + 0.02)^9$

First, calculate $(1 + 0.02)^9$:
$(1.02)^9 \approx 1.19509303$

Then, multiply by the principal:
$A = 110 	imes 1.19509303 \approx 131.46$

# Answer:
The total value of the investment is approximately $\$131.46$.

### Problem 15: $90 at 4% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 90$, $r = 4\% = 0.04$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 90(1 + 0.04)^2$

First, calculate $(1 + 0.04)^2$:
$(1.04)^2 = 1.0816$

Then, multiply by the principal:
$A = 90 	imes 1.0816 = 97.344$

# Answer:
The total value of the investment is approximately $\$97.34$.

### Problem 16: $34,300 at 2% compounded annually for 7 years
# Explanation:
## Step 1: Identify the values
$P = 34300$, $r = 2\% = 0.02$, $t = 7$

## Step 2: Apply the compound interest formula
$A = 34300(1 + 0.02)^7$

First, calculate $(1 + 0.02)^7$:
$(1.02)^7 \approx 1.1486856$

Then, multiply by the principal:
$A = 34300 	imes 1.1486856 \approx 39400.02$

# Answer:
The total value of the investment is approximately $\$39400.02$.

### Problem 17: $29,800 at 4% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 29800$, $r = 4\% = 0.04$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 29800(1 + 0.04)^2$

First, calculate $(1 + 0.04)^2$:
$(1.04)^2 = 1.0816$

Then, multiply by the principal:
$A = 29800 	imes 1.0816 = 32231.68$

# Answer:
The total value of the investment is $\$32231.68$.

### Problem 18: $35,900 at 7% compounded annually for 4 years
# Explanation:
## Step 1: Identify the values
$P = 35900$, $r = 7\% = 0.07$, $t = 4$

## Step 2: Apply the compound interest formula
$A = 35900(1 + 0.07)^4$

First, calculate $(1 + 0.07)^4$:
$(1.07)^4 \approx 1.31079601$

Then, multiply by the principal:
$A = 35900 	imes 1.31079601 \approx 47057.58$

# Answer:
The total value of the investment is approximately $\$47057.58$.

### Problem 19: $46,600 at 16% compounded annually for 2 years
# Explanation:
## Step 1: Identify the values
$P = 46600$, $r = 16\% = 0.16$, $t = 2$

## Step 2: Apply the compound interest formula
$A = 46600(1 + 0.16)^2$

First, calculate $(1 + 0.16)^2$:
$(1.16)^2 = 1.3456$

Then, multiply by the principal:
$A = 46600 	imes 1.3456 = 62704.96$

# Answer:
The total value of the investment is $\$62704.96$.

### Problem 20: $11,700 at 14% compounded annually for 4 years
# Explanation:
## Step 1: Identify the values
$P = 11700$, $r = 14\% = 0.14$, $t = 4$

## Step 2: Apply the compound interest formula
$A = 11700(1 + 0.14)^4$

First, calculate $(1 + 0.14)^4$:
$(1.14)^4 \approx 1.74900625$

Then, multiply by the principal:
$A = 11700 	imes 1.74900625 \approx 20463.37$

# Answer:
The total value of the investment is approximately $\$20463.37$.

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QUESTION IMAGE

Question

Explanation:

Problem 1: $420 at 3% compounded annually for 4 years

Step 1: Identify the values

Step 2: Apply the compound interest formula

Step 1: Identify the values

Step 2: Apply the compound interest formula

Step 1: Identify the values

Step 2: Apply the compound interest formula

Answer:

Problem 2: $215 at 6% compounded annually for 2 years