Question

1. How long will it take to double the investment if compounded quarterly at 20% (hint: graph )

Steve invest 10,000 today for 12 years with an interest rate of 12.5 %

Answer 1

GIVEN:

Principal investment at the beginning = $10000

Interest rate compounded quarterly = 12.5%/4 = 0.125/4 = 0.03125

Double the investment, Amount = $20000.

Now, we need to calculate that how long it will take to double the investment.

Let our Desired Future value = $20000

Formula,

Future value (FV) = P(1+i)n

where P - Principal investment = $10000, i - interest rate = 0.03125

we need to calculate 'n' - no. of quarterly periods

=> $20000 = $10000(1+0.03125)n

=> (1.03125)n = $20000/$10000

=> (1.03125)n = 2

we can written 2 as (1.03125)24

=> (1.03125)n = (1.03125)24

Applying mathematical rule that bases are equal, so the powers are also equal.

=> No. of quarterly periods (n) = 24

Therefore,

No. Of years = 24/4 = 6 years

IT TAKES 6 YEARS TO DOUBLE THE INVESTMENT IF COMPOUNDED QUARTERLY

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