Question

Find the interest rates in the following situations.

a. APR = 8%, compounded monthly. Find the effective annual interest rate.

b. Nominal rate is 10% compounded quarterly. Find the effective semiannual rate.

c. The effective annual interest rate is 11.02% and compounding is monthly. Find the nominal interest rate.

d. r = 6% and compounding is monthly. Find the effective quarterly interest rate.

Answer 1

a.

Effective interest rate = (1+0.08/12)^12 -1

= (1+0.00666667)^12 -1

= (1.00666667)^12 -1

= 0.082999 ~ 8.30%

b.

Effective semiannual interest rate = (1+ 0.1 / 4)^2 -1

= (1+ 0.025)^2 -1

= (1.025)^2 -1

= 0.050625 ~ 5.06%

c.

Let monthly interest rate be i%, then as per given condition

(1+i%)^12 - 1 = 0.1102

(1+i%)^12 = 1.1102

(1+i%) = 1.1102^(1/12) = 1.0087497

i = 1.0087497 - 1 = 0.0087497

APR = 0.0087497 * 12 = 0.1049964 ~ 10.5%

d.

Effective quarterly interest rate = (1 + 0.06 / 12)^3 - 1

= (1 + 0.005)^3 - 1

= (1.005)^3 - 1

= 0.015075125 ~ 1.507% ~ 1.51%