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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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