Question

Doris Wade purchased a condominium for ​$50 comma 000 in 1984. Her down payment was ​$7,000. She financed the remaining amount as a ​$43,000​, 35​-year mortgage at 6​%, compounded monthly. Her monthly payments are ​$200. It is now 2009 ​(25 years​ later) and Doris has sold the condominium for ​$100,000​, immediately after making her 300th payment on the unit. Find her effective annual internal rate of return on this investment.

Answer 1

Initial cost is 7000. Monthly payment is 200 for 25*12 = 300 months at 0.5%. The salvage value is 100,000. Doris has to pay the remaining balance on the loan account as well. If total period is 35*12 = 420 months and she has paid instalments for 300 periods then the balance payment with 420 – 300 = 120 periods left, is given by Bn = 200(P/A, 0.5%, 120) = 200*90.073453 = 18014.70. This amount has to be paid now.

Find the effective monthly rate so that NPV (at the time of purchase) = 0

0 = -7000 - 200(P/A, i%, 300) + (100,000 - 18014.70)(P/F, i%, 300)

= -7000 - 200(P/A, i%, 300) + 81985.30(P/F, i%, 300)

Try for i% = 0.1%.

NPV = 1931.16

Try for i% = 0.2%

NPV = -7064.50

Use interpolation for finding the effective monthly rate

ie% = 0.1% + (0.2% - 0.1%)*(1931.16/(1931.16+7064.50)) = 0.12147% per month or 1.458%.