Question

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $25,000

after 10
years with an APR of 11%
compounded monthly. Round your answer to the nearest cent, if necessary.

Answer 1

Explanation:

To calculate the present value (PV), you can use the formula for the present value of a future sum with compound interest:

PV = FV / (1 + r/n)^(nt)

Where:

PV = Present Value (the amount you need to invest now)

FV = Future Value (which is $25,000)

r = Annual Interest Rate (11% or 0.11)

n = Number of times the interest is compounded per year (monthly, so n = 12)

t = Number of years (10 years)

Now, plug in these values into the formula:

PV = $25,000 / (1 + 0.11/12)^(12*10)

PV = $25,000 / (1 + 0.00916667)^(120)

PV ≈ $25,000 / (1.00916667^120)

PV ≈ $25,000 / 1.35637439

PV ≈ $18,428.41 (rounded to the nearest cent)

So, you would need to invest approximately $18,428.41 now in one lump sum to have $25,000 after 10 years with an APR of 11% compounded monthly.