Question

2.30 For a 15 percent effective annual interest rate, what is the nominal interest rate if (a) Interest is compounded monthly? (b) Interest is compounded daily (assume 365 days per year)? (c) Interest is compounded continuously?

Answer 1

r = nominal interest rate

i = effective interest rate

m = compounding period

r = m × [ ( 1 + i)^1/m - 1 ]

i = 15%

a) m = 12

r = 12*[(1+ 0.15)^1/12 - 1] = 0.140579 = 14.058%

b) m = 365

r = 365*[(1+0.15)^1/365 -1 ] = 0.13978 = 13.98%

c) for continuous compounding, formula is

i = e^r -1

0.15 = e^r - 1

1.15 =e^r

ln 1.15 = r

0.13976 = r

r = 13.98%