Question

Sally lends 10,000 to Tim. Tim agrees to pay back the loan over 5 years with monthly

payments payable at the end of each month. Sally can reinvest the monthly payments from

Tim in a savings account paying interest at 6%, compounded monthly. The yield rate earned

on Sallys investment over the five-year period turned out to be 7.45%, compounded semi-

annually. What nominal rate of interest, compounded monthly, did Sally charge Tim on the

loan?

Answer 1

Answer:

Amount lended to Tim = $10,000

Monthly repayments = 60

Interest earned on savings account = 6% compounded monthly

5-Year Yield = 7.45% compounded semi annually

Total amount received at the end of 5 years (inclusive of interest on loan & saving accounts) = Amount * (1+(Yield% / 2)^{Number of years * 2}

Total amount received at the end of 5 years = $10,000 * (1+7.45%/2)^5*2

Total amount received at the end of 5 years = $14,415.66

Now, we need to identify the interest charged on Tim's loan. This can be calculated using the goal seek function in excel. Excel > Data > What if analysis > Goal Seek

Note: Montly installments are calculated using PMT function in excel =pmt(rate,nper,pv)

By running goal seek we'll get the following output:

Nominal rate of interet charged by Sally to Tim was 8.59% compounded monthly.