A borrower has L = $238,000. She makes loan interest payments at the end of each

Question

A borrower has L = $238,000. She makes loan interest payments at the end of each 6month period for N=8 years with loan interest computed using an annual effective discount rate of d = 6.5%.   Each time (i.e., every 6 months) she makes the required interest payment, she in addition deposits into a sinking fund earning a nominal annual interest rate of 4.2% convertible monthly. The amount of each sinking fund deposit is D for the first 3 years (i.e., 6 total deposits each of D) and then 2D for each deposit for the remaining 5 years, at which point the amount in the sinking fund equals L. Find D.

Explanation / Answer

It will equal at the end of 7 year.

Finding D:

D * [(1+r)^n-1]/r + 2D * [(1+r)^n-1]/r = 238000

D * [(1+.042/12)^6-1]/(.042/12) + 2D * [(1+.042/12)^10-1]/(.042/12) = 238000

6.05274D + 2D * 10.15898 = 238000

D = 238000 / 26.370704

D = 9025.17

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