Question

You will deposit $300 per year for the next 5 years. You expect the interest rate 1 year from now to be 8%, 2 years from now to be 8%, 3 years from now to be 12%, and 4 years from now to be 9%. If your forecast of interest rates is correct, how much money will you have 5 years from now?

Round your answer to 2 decimal places, for example 100.12.

Answer 1

First $300 will be deposited in year 1 and will earn interest at 8% for 4 years. second $300 will be deposited in year 2 and will earn interest at 8% for 3 years. third $300 will be deposited in year 3 and will earn interest at 12% for 2 years. forth $300 will be deposited in year 4 and will earn interest at 9% for 1 year. fifth $300 will be deposited in year 5 and will not earn any interest.

Here assumption is that $300 will be deposited at the end of each year.

Future value of year 1 deposit = present value*(1+interest rate)^{no. of years} = $300*(1+0.08)⁴ = $300*1.08⁴ = $300*1.36048896 = $408.146688

Future value of year 2 deposit = $300*1.08³ = $300*1.259712 = $377.9136

Future value of year 3 deposit = $300*1.12² = $300*1.2544 = $376.32

Future value of year 4 deposit = $300*1.09¹ = $300*1.09 = $327

Year 5 deposit = $300

money will you have 5 years from now = $408.146688 + $377.9136 + $376.32 + $327 + $300 = $1,789.38