Question

Bob and Carol and Ted and Alice are to share a 100 payment annuity-immediate with monthly payments of $500. Bob will receive his payments, then Carol, then Ted and finally Alice. The annuity is valued using a nominal annual interest rate of 12% compounded monthly. They are to split the annuity equally. How many payments does Ted receive?

Answer 1

In this question, we have the following variables:

Payment amount/ Recurring payment : $500

No. of periods: 100

Interest rate: 12% compounded monthly

Present value = 0

Using the formula for Future value= FV(rate, no. of periods, an amount per month, present value, a beginning of the year) in excel or spreadsheets online by Google.

Now values would be = FV( 12%/12, 100, -500, 0, 0)

12%/12 = For monthly compounding

100= Periods

-500= Outflow, hence minus 500 here.

0= Present value, since there is no initial investment amount. Only the payments are being on a recurring basis

0= Beginning of year

The value arrives at is $85240.69. Since, it has been mentioned that they shall be splitting the annuity equally, the amount recieved by Ted would be 21,310.17.