Question

Effective Rate Find the effective rate of interest corresponding to a nominal rate of 6% par year compounded (a) annually, (b) semiannually, (c) quarterly, and (d) monthly.

Answer 1

compounded (a) annually = 6 %

compounded (b) semiannually = 6.09 %

compounded (c) quarterly = 6.14 %

compounded (d) monthly = 6.17 %

Explanation:

given data

nominal rate = 6% par year = 0.06

solution

we know effective rate of interest is express as

effective rate of interest =
`(1+(r)/(n))^n` - 1 .................1

here r is rate and n is no of compound period

so for compounded annually put here value n = 1

effective rate of interest =
`(1+(r)/(n))^n` - 1

effective rate of interest =
`(1+(0.06)/(1))^1` - 1

effective rate of interest = 0.06 = 6 %

and

now we get compounded semiannually put here value n = 2

effective rate of interest =
`(1+(r)/(n))^n` - 1

effective rate of interest =
`(1+(0.06)/(2))^2` - 1

effective rate of interest = 0.0609 = 6.09 %

and

now we get compounded quarterly put here value n = 4

effective rate of interest =
`(1+(r)/(n))^n` - 1

effective rate of interest =
`(1+(0.06)/(4))^4` - 1

effective rate of interest = 0.061364 = 6.14 %

and

now we get compounded monthly put here value n = 12

effective rate of interest =
`(1+(r)/(n))^n` - 1

effective rate of interest =
`(1+(0.06)/(12))^(12)` - 1

effective rate of interest = 0.061678 = 6.17 %