Question

John deposited an amount of $1000 in a bank. Seven years later, John went to the bank and found that his account increased to $2000. (a) If the bank pays the interest continuously, what are the nominal interest rate and the effective interest rate per year? (b) If the bank pays the interest per month, what are the nominal and effective interest rates per year.

Answer 1

Future worth = F = $2000

Present worth = P = $1000

Tenure = 7 years

a) Interest payed continuously

We have Ieff = e^r– 1

Where Ieff = Effective interest rate & r = Nominal interest rate

F = P (1 + Ieff)^n

2000 = 1000 (1 + e^r– 1)^7

2 = (1 + e^r– 1)^7

Solving the above equation

r = 0.16

r = 16%

ieff = e^r– 1

ieff = e^0.16– 1

ieff = 0.1735 = 17.35%

a) Interest payed per month

We have Ieff = [1+r/m]^m -1

Where Ieff = Effective interest rate, r = Nominal interest rate & m = 12 [12 months in a year]

F = P (1 + Ieff)^n

2000 = 1000 (1 + {[1+r/m]^m -1})^7

2 = (1 + {[1+r/12]^12 -1})^7

Solving the above equation

r = 0.099

r = 9.9%

ieff = [1+r/m]^m -1

ieff = [1+0.099/12]^12 -1

ieff = 0.1036 = 10.36%