Question

ABC plans to make equal payments into a fund on 1/1 of each year, beginning on 1/1/A with the final payment on 1/1/D, to pay the principal (only) of serial bonds maturing $50,000 on 12/31/C and $50,000 on 12/31/D. How much must be deposited annually if the fund earns 10%? Show work.

Ans: $20,568 annually

Answer 1

Solution:

Let amount to be deposited annually = X

Now present value of X = Present value of bond repayment at the end of 3rd year and 4th year

X * Cumulative PV factor at 10% for 4 periods of annuity due = $50,000 * PV factor at 10% for 3rd period + $50,000 * PV factor at 10% for 4th period

3.48685 X = $50,000 * 0.751315 + $50,000 * 0.683013

3.48685 X = $71,716.41

X = $20,568