Question

If you deposited $1000 in a bank and were paid a series of uniform payments of $50 at 3.5% per payment period, how many payments would you receive? How many payments would you receive at 1.5%?

Answer 1

P = 1000

A = 50

i = 3.5%

n= ?

1000 = 50*(P/A,3.5%,n)

(P/A,3.5%,n) = 20

((1 + 0.035)^n-1)/(0.035*(1 + 0.035)^n) = 20

(1.035)^n = 20 * 0.035*(1.035)^n + 1

(1-0.7)*(1.035)^n = 1

(1.035)^n = 1/0.3 = 3.3333

taking log both sides

n = log 3.3333 / log 1.035

n = 34.99 periods = 36 periods

When i = 0.015

(P/A,1.5%,n) = 20

((1 + 0.015)^n-1)/(0.015*(1 + 0.015)^n) = 20

(1.015)^n = 20 * 0.015*(1.015)^n + 1

(1-0.3)*(1.015)^n = 1

(1.015)^n = 1/0.7 = 1.428571

taking log both sides

n = log 1.428571 / log 1.015

n = 23.96 periods = 24 periods