Question

lesson quiz 3-6
name

1. samson opened a bank account with 1.25% simple interest. the total amount of interest samson will earn after 20 years is $812.50. how much did samson deposit when he opened the account?
2. which equation represents the total interest, t, earned when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10? solve.

a. t = 100 • (10 + 0.1)
b. t = 100 • (10 + 0.01)
c. t = 100 • 0.1 • 10
d. t = 100 • 0.01 • 10

1. mika opened a bank account that earns simple interest with an initial deposit of $2,200. she made no other transactions throughout the year. at the end of the year, mika had $2,260.50 in her account. what was the simple interest rate?

q 3-6 copyright © by savvas learning company llc. all rights reserved

Explanation:

Step1: Recall simple interest formula

The total amount for simple interest is $A = P(1 + rt)$, where $A$ is total amount, $P$ is principal, $r$ is annual rate, $t$ is time in years.

Step2: Isolate principal $P$

Rearrange formula: $P = \frac{A}{1 + rt}$
Substitute $A=\$812.50$, $r=0.0125$, $t=20$:
$P = \frac{812.50}{1 + (0.0125 \times 20)}$

Step3: Calculate denominator

$0.0125 \times 20 = 0.25$; $1 + 0.25 = 1.25$

Step4: Solve for $P$

$P = \frac{812.50}{1.25} = 650$

---

Step1: Recall simple interest formula

Total interest $T = P \times r \times t$, where $P$ is principal, $r$ is annual rate, $t$ is time.

Step2: Substitute given values

$P=\$100$, $r=0.01$, $t=10$:
$T = 100 \times 0.01 \times 10$
Match to option D, calculate:
$T = 100 \times 0.01 \times 10 = 10$

---

Step1: Calculate earned interest

Interest $I = \text{Final amount} - \text{Principal}$
$I = 2260.50 - 2200 = 60.50$

Step2: Rearrange simple interest formula

$r = \frac{I}{P \times t}$, where $I$ is interest, $P=\$2200$, $t=1$

Step3: Solve for $r$

$r = \frac{60.50}{2200 \times 1} = 0.0275$
Convert to percentage: $0.0275 \times 100 = 2.75\%$

Answer:

1. $\$650$
2. D. $T = 100 \bullet 0.01 \bullet 10$; Total interest earned is $\$10$
3. $2.75\%$