Question

In three years you will pay the first of eight annual $100 payments. The current interest rate is 14%, but after 5 years (by t=5) the rate will have dropped to 8%. What is the total value of your payments at the end of 10 years?

I know the answer is $1092, however, I am struggling in how to split my interest rates. If anyone can give me the steps that would be greatly appreciated.

Answer 1

- In three years from now you will pay the first of eight annual $100 payments till year end 10 which means that you will pay 8 paymnets in 7 years

- The current interest rate is 14% which is for the first 5 years.

Calculating the Future Value at yer end 5 of annuity paymnet made at year 3 and year 4 using annuity due formula:-

Where, C= Periodic Payments = $100

r = Periodic Interest rate = 14%

n= no of periods = 2

Future Value at year end 5 is $243.96

Since from year 5 the Interest rate is changed to 5%, the above amount will only earn Interest at 8% till year 10

- Future Value till year end 10 = Future Value at year end 5*(1+r)^5

Where,

r = Periodic Interest rate = 8%

Future Value till year end 10 = $243.96*(1+0.08)^5 = $243.96*1.4693280768

Future Value till year end 10 = $358.46

- Now for the last 6 payments which starts from year end 5 till year end 10 which means that you will pay 6 paymnets in 5 years

Calculating the Future Value of first 5 payments using Annuity due formula and adding the year end 10 payment as it will not earn any interest.

Where, C= Periodic Payments = $100

r = Periodic Interest rate = 8%

n= no of periods = 5

Future Value = $733.59

- Total Future Value = $358.46 + $733.59

Total Future Value = $1092.05

So, the total value of your payments at the end of 10 years is $1092.05

If you need any clarification, you can ask in comments.    

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