Question

You invest $12,000 now and get $14,000 back in 7 years.

(A) What nominal interest rate convertible every four months did you earn?

(B) What nominal discount rate compounded semi-annually did you earn?

(C) What annual effective rate of discount did you earn?

Answer 1

Amount Invested = $12,000

Future Value in 7 years = $14,000

a). Calculating the nominal interest rate convertible every four months:-

Where, Invested amount = $12,000

r = Interest rate

n= no of periods = 7 years

m = no of times compounding in a year = 12 months/4 months = 3

Taking 21-root on both sides,

1.00736752 = (1+r/3)

r = 2.2103%

So, nominal interest rate convertible every four months is 2.2103%

b). Calculating the nominal discount rate compounded semi-annually:-

Where, Invested amount = $12,000

r = Interest rate

n= no of periods = 7 years

m = no of times compounding in a year = 2

Taking 14-root on both sides,

1.0110716 = (1+r/2)

r = 2.2143%

So, nominal discount rate compounded semi-annually is 2.2143%

c). Calculating the annual effective rate of discount:-

Where, Invested amount = $12,000

r = Interest rate

n= no of periods = 7 years

m = no of times compounding in a year = 1

Taking 7-root on both sides,

1.0222658 = (1+r)

r = 2.2266%

So, annual effective rate of discount is 2.2266%

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