Question

Suppose you have an opportunity to invest in a fund that pays 13​% interest compounded annually.​ Today, you invest ​$5,000 into this fund. Three years later​ (EOY 3), you borrow $2500 from a local bank at 10​% annual interest and invest it in the fund. Two years later​ (EOY 5), you withdraw enough money from the fund to repay the bank loan and all interest due on it. Three years from this withdrawal​ (EOY 8) you start taking ​$1000 per year out of the fund. After five withdrawals of $1000 have withdrawn your original $5000. The amount remaining in the fund is earned interest. How much remains?

What is the amount withdrawned at the EOY 5?

Please show all work.

Answer 1

interest rate on deposit = 13%

5000 deposited into this account initially and 2500 deposited into this into EOY 3

Total amount in this account at EOY 5 = 5000 * (1+0.13)^5 + 2500 *(1+0.13)^2

= 12404.43

Now 2500 was taken on loan at 10% in EOY3 and is repaid back in EOY5

Amount paid back in EOY 5 to repay the loan = 2500 (1+0.1)^2 = 3025

Amount left in account after loan repayment = 12404.43-3025 = 9379.43

This amount sits undisturbed till EOY 8 (3 years from EOY 5)

Amount in EOY 8 in account = 9379.43 *(1+0.13)^3 = 13533.55

amount of 1000 is withdrawn from the account at EOY8, so net amount left at EOY 8 = 13533.55-1000 = 12533.55

Now four more withdrawals are made of 1000 each.year

The present value of this annuity withdrawl at EOY 8 = 1000 *(P/A,13%,4)

= 1000 * 2.974471 = 2974.47

Now equivalent amount left after subtracting present value of withdrawals at EOY 8

= 12533.55 - 2974.47 = 9559.079

Now the future value of this net value at the EOY 12 = 9559.079 * (F/P, 13%,4)

= 9559.079 * 1.630473 = 15585.82

This is the interest accumulated into the account at EOY 12

Amount withdrawn in EOY5 = 3025

Pls comment if you require any further explanation.