Question

josue invested $160 in an account paying an interest rate of 1.8% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 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

$r = \frac{1.8\%}{100} = 0.018$

Step3: Plug values into formula

$A = 160(1 + 0.018)^5$

Step4: Calculate the growth factor

First compute $1 + 0.018 = 1.018$, then $1.018^5 \approx 1.09329$

Step5: Compute final amount

$A = 160 \times 1.09329 \approx 174.926$

Step6: Round to nearest dollar

Round $174.926$ to the nearest whole number.

Answer:

$175$