Question

A debt of $3000 due six years from now is instead to be paid off by three payments: $500 now, $1500 in three years, and a final payment at the end of five years. What would this payment be if an interest rate of 6% compounded annually is assumed?

Answer 1

5 years

Explanation:

Let the focal date be today
i = r = 6% = 0.06

Sum of the values of old Obligations} _ {sum of the values of new obligations

3,000 (1.06)^-6 = 500 + 1,500 (1.06)^-3 + 475 (1.06)^-n
3,000 x 0.705 = 500 + 1,500 x 0.8396 + 475 (1.06)^-n
2,115 = 500 + 1,259 + 475 (1.06)^-n
475 (1.06)^-n = 356
1.06^-n = 356/475
(1.06)n = 1.3343
Taking log on both sides
n log 1.06 = log 1.3343
log 1.3343
n = log 1.06
0.1252
n = 0.0253
n = 4.95 .. 5 years
The value of n is 5 years