Question

harper is going to invest in an account paying an interest rate of 4.5% compounded monthly. how much would harper need to invest, to the nearest hundred dollars, for the value of the account to reach $96,000 in 5 years?

Answer 1

To calculate the amount that Harper would need to invest, we can use the formula for compound interest. Plugging in the given values, Harper would need to invest approximately $78,493 for the account value to reach $96,000 in 5 years.

Step-by-step explanation:

To calculate the amount that Harper would need to invest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the future value of the investment ($96,000 in this case)
• P is the principal amount Harper needs to invest
• r is the annual interest rate (4.5%)
• n is the number of times interest is compounded per year (12, since it's compounded monthly)
• t is the number of years of the investment (5)

Plugging in these values into the formula, we can solve for P:

P = A / (1 + r/n)^(nt)

P = $96,000 / (1 + 0.045/12)^(12*5)

P ≈ $78,493

Therefore, Harper would need to invest approximately $78,493 for the value of the account to reach $96,000 in 5 years.