Question

A loan of $12,000 is being repaid with payments of $1,500 at the end of each year for 10 years. These payments can earn interest at an effective rate of 6% per annum. At the end of the year, this interest is reinvested at the annual effective rate 5% for the first 6 years and only 4% for the second 4 years. Find the yield rate over the 10-year period.

Answer 1

1st payment will be received at the end of 1st year

Therefore, interest will be earned from 2nd year onwards.

Interest on 1st payment will be received at the end of 2nd year

And therefore, interest on interest will be earned from 3rd year onwards.

Simple Interest will be 6% on 1500 every year end for 9 years = 1500×0.06×9 = $810

Interest on Interest will be as follows:

Therefore, Interest on Interest is $873.96

Total Interest earned on payments from year 1 to 10

= Simple Interest + Interest on Interest

= 810 + 873.96 = $1683.96

Therefore, Yield Rate over 10 year period

= [(Total return earned i.e. All payments + Total Interest)-Loan]/Loan

= [{(1500×12) + 1683.96}-12000]/12000 = 64.033%

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