Question

What is the nominal annual rate of interest compounded quarterly if a loan of $ 25,000 is repaid in seven years by payments of $2000 made at the end of every six months?

Answer #1

Loan amount = $25,000

Semiannual payment = $2,000

Number of payments = 14 (7 years)

Let semiannual interest rate be i%

$25,000 = $2,000 * PVIFA(i%, 14)

Using financial calculator:

N = 14

PV = 25000

PMT = -2000

FV = 0

I = 1.5485%

Semiannual interest rate = 1.5485%

Effective annual rate = (1 + Semiannual interest rate)^2 -
1

Effective annual rate = (1 + 0.015485)^2 - 1

Effective annual rate = 1.03121 - 1

Effective annual rate = 0.03121 or 3.121%

Quarterly interest rate = (1 + Effective annual rate)^(1/4) -
1

Quarterly interest rate = (1 + 0.03121)^(1/4) - 1

Quarterly interest rate = 1.007713 - 1

Quarterly interest rate = 0.007713 or 0.7713%

Annual interest rate = 4 * Quarterly interest rate

Annual interest rate = 4 * 0.7713%

Annual interest rate = 3.085% or 3.09%

Therefore, nominal annual interest rate is 3.09% compounded quarterly

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