Question

a.       The effective interest rate is 21.44%. If there are 12 compounding periods per year, what is the nominal interest rate?

b.      What is the effective interest rate on a continuously compounded loan that has a nominal interest rate of 25%?

c.       Which is the better investment, a fund that pays 20% compounded annually, or one that pays 18.5 % compounded continuously?

d.      Money invested at 6% per year, compounded monthly. How money months you need to triple your money?

e.       One thousand dollars is deposited into an account that pays interest monthly and allowed to remain in the account for three years. The balance at the end of the three years is $1,544.00. What is the nominal interest rate paid on this account?

Answer 1

a.

what is the nominal interest rate=((1+21.44%)^(1/12)-1)*12=19.58%

b.

effective interest rate=e^(25%)-1=28.40%

c.

effective rate 18.5 % compounded continuously=e^(18.5%)-1=20.32%

so 18.5 % compounded continuously is better investment as return is above 20%.

d.

FV=PV*(1+r)^n

3=1*(1+(6%/12))^(n*12)

1.005^(n*12)=3

use natural log

12n=ln(3)/ln(1.005)

n=(ln(3)/ln(1.005))/12

n=18.36 years or 220.27 months

e.

What is the nominal interest rate paid on this account=((1544/1000)^(1/36)-1)*12=14.57%

the above is answer..