How long will it take a given sum of money (Say in Rupees) to increase 4 times its present
value when compounded half yearly at 7% rate of interest?
Solution:
Formula: "A = P [1+i ]^{N\\times T}"
Where:
A= 4, P=1, i= 0.035 N = 2
T =?
Find "i = \\frac{0.07}{2} = 0.035"
Insert the figures into the formula:
"4 = 1 [1+0.035]^{2\\times T}"
"[1+0.035]^{2\\times T} =4"
"[1.035]^{2\\times T} =4"
"(1.071225) ^{T} =4"
Use logarithms on both sides:
Tlog1.071225 = log4
"T = \\frac{log4}{log1.071225}"
"T = 20.14\\; years" = 20 years and 1.5 months
It will take approximately 20 years and one and a half months for a given sum of money to increase 4 times its present value when compounded half yearly when compounded half yearly at 7% interest rate.
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