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%?
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
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