Question

How long will it take (in years) to earn $75,000 in interest if $100,000 is deposited at a 5% continuous compounded rate? If you require $125,000 in five years time, did you deposit enough money?

Answer 1

Answer a.

Amount deposited = $100,000
Future value = $175,000
Interest rate = 5% compounded continuously

Amount deposited * exp(Interest rate * Time period) = Future value
$100,000 * exp(0.05 * Time period) = $175,000
exp(0.05 * Time period) = 1.75
0.05 * Time period = ln(1.75)
0.05 * Time period = 0.559616
Time period = 11.19 years

Answer b.

Amount deposited = $100,000
Interest rate = 5% compounded continuously
Time period = 5 years

Future value = Amount deposited * exp(Interest rate * Time period)
Future value = $100,000 * exp(0.05 * 5)
Future value = $100,000 * 1.2840254
Future value = $128,402.54

Yes, you have deposited enough money today