Question

An investor makes a deposit today and earns a force of interest of 13% over the next five years. What force of interest must be earned over the subsequent five years in order to triple the investment at the end of ten years?

Answer 1

Let investor make investment of $1 and target value is $3.

PV = $1; Target value = $3

Interest rate for first 5 years = Rate1 = 13%

Now, lets calculate the value for investment in first 5 years:

Value of investment after 5 years or say, FV1 = PV x (1+Rate1)^Years

FV1 = 1 x (1+13%)^5

FV1 = $ 1.842435

Hence, value in first 5 years will grow up to = $ 1.842435

.

Now, let’s calculate interest rate required for next 5 years to triple the investment:

Rate of interest for next 5 years = Rate2

Rate2 = (Target value / FV1)^(1/5) - 1

Rate2 = ( $3 / $1.842435 )^(1/5) - 1

Rate2 = 1.102417 - 1

Rate2 = Rate for subsequent 5 years = 10.2417%