Question

An investment that currently sells for $200 makes payments every year forever, which grow annually at a constant rate. If the annual return on this investment is 6% and next payment amount is $10, what is the constant rate at which the payments grow annually? At an annual interest rate of 7%, how many years does it take to triple your money?

Answer 1

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Present Value of perpetuity = $200

P = next payment = $10

r = Annual interest rate = 6%

Let g = growth rate

Present Value of Perpetuity = P / (r - g)

$200 = $10 /(6% - g)

6% - g = 0.05

g = 1%

Therefore, constant growth rate is 1%

>>>>>>>>

FV = Future Value = $3

PV = Present Value = $1

r = interest rate = 7%

Let n = number of years

FV = PV * (1+r)^n

$3 = $1 * (1+7%)^n

(1.07)^n = 3

n = log (3) / log(1.07)

n = 0.477121255 / 0.0293837777

n = 16.2375737

Therefore, it will take 16.24 years to triple the money