Question

Karen wants to have $26,689 in her investment account in 6 years. If her bank offers an annual compound interest rate of 2.4% with monthly compounding, how much should she deposit today?

Round your answer to the nearest dollar.

Answer 1

$20,210.98

Explanation:

To calculate the amount Karen should deposit today, we can use the formula for compound interest:

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

where A is the amount of money in the account after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we want to find the value of P that will give us A = $26,689 in t = 6 years, with an annual interest rate of r = 0.024 (2.4% as a decimal) and monthly compounding, which means n = 12.

So we can plug in these values into the formula and solve for P:

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

P = 26689 / (1 + 0.024/12)^(12*6)

P = $20,210.98

So, the answer is $20,210.98