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Calculating the effective annual interest rate

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If you barrow \$4,000 at \$500 interest for one year, What is your effective interest rate for the following payment plans?

a. Annual payment.
b. Semiannual payment.
c. Quarterly payment.
d. Monthly payment.

SOLUTION This solution is FREE courtesy of BrainMass!

If you barrow \$4,000 at \$500 interest for one year, What is your effective interest rate for the following payment plans?

a. Annual payment.
Annual number of payments=1
Interest=\$500
Total number of payments=1
Principal=\$4000

Effective interest rate=(2*Annual number of payments*Interest)/((Total number of payments+1)*Principal)
=(2*1*500)/((1+1)*4000)=12.5%

b. Semiannual payment.
Annual number of payments=2
Interest=\$500
Total number of payments=2
Principal=\$4000

Effective interest rate=(2*Annual number of payments*Interest)/((Total number of payments+1)*Principal)
=(2*2*500)/((2+1)*4000)=16.67%

c. Quarterly payment.
Annual number of payments=4
Interest=\$500
Total number of payments=4
Principal=\$4000

Effective interest rate=(2*Annual number of payments*Interest)/((Total number of payments+1)*Principal)
=(2*4*500)/((4+1)*4000)=20.00%

d. Monthly payment.
Annual number of payments=12
Interest=\$500
Total number of payments=12
Principal=\$4000

Effective interest rate=(2*Annual number of payments*Interest)/((Total number of payments+1)*Principal)
=(2*12*500)/((12+1)*4000)= 23.08%

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