Question

M. Oocher borrows $15,000 from Al Ender.  The debt is to be repaid quarterly over 6.5 years.  If the money is lent at a nominal rate of 4.4% per year, compounded 4 times per year, what are the periodic payments at the end of each 3-months?

Answer 1

Given

Borrowed Amount = $ 15000

Time period = 6.5 Years

Nominal interest rate = 4.4% Compounded Quarterly

Rate of interest per Quarter = 4.4% /4 = 1.1%

In a Year there are 4 Quarters.

No.of Quarters in 6.5 Years = 6.5*4= 26 Quarters

We know that Present Value of Annuity = C [ {1-( 1+i) ^ -n}/i]

Here C = Cash flow per period

I = Rate of interest

n = No.of payments

We also know that present value of the future payments is equal to the loan amount.

$ 15000= C [ { 1-( 1+0.011)^-26}/0.011]

$ 15000= C [ { 1-( 1.011)^-26 }/0.011]

$ 15000= C [ { 1-( 0.752437)} /0.011]

$ 15000= C [ { 0.247563/0.011]

$ 15000=C *22.50576

$ 15000/22.50576=C

C = $ 666.4961

Hence the periodic payment is $ 666.4961.

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