Question

2) What annuity paid at the end of each 9-month period can accumulate $ 10,000 at the end of the tenth month, if interest is considered at the rate of 17% convertible each month?

Answer 1

Answer-

This prroblem has to be divided into two parts

The first part [ From year 9 to 10 ]

Future value = $ 10000
Interest rate = 17 % = 17 % / 12 = 1.41667 % [ covertible each month]
Number of periods = N = 1 month = 1
PMT = 0
PV = ?

Present value = PV = $ 9860.312 [ The amount at the beginning of 9th month]

The second part [ from year 1 to 9]

Here the Present value from previous calculation is the Future Value (FV) at the end of year 9.

FV = $ 9860.312
Interest rate = I/Y = 1.41667 %
Number of periods = N = 9 months = 9
present value = PV = $ 0
Annuity paid = PMT = ?

Annuity paid each year = PMT = $ 1034.962

Therefore the annuity paid at the end of each 9-month period = $ 1034.962 / month