Question

christopher invested $1,000 in an account paying an interest rate of 5.8% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 7 years?

Explanation:

Step1: Recall compound interest formula

The formula for compound interest (annual compounding) is $A = P(1 + r)^t$, where:

• $A$ = final amount
• $P$ = principal amount
• $r$ = annual interest rate (decimal)
• $t$ = time in years

Step2: Convert rate to decimal and define values

$P = 1000$, $r = \frac{5.8}{100} = 0.058$, $t = 7$

Step3: Substitute values into formula

$A = 1000(1 + 0.058)^7$

Step4: Calculate the growth factor

First compute $1.058^7 \approx 1.4881$

Step5: Compute final amount

$A \approx 1000 \times 1.4881 = 1488.1$

Step6: Round to nearest dollar

Round $1488.1$ to the nearest whole number.

Answer:

$\$1488$