The amount that the investment will earn if it is compounded continuously at the same interest rate for 10 years is $63,891.55.
How the earnings are determined:
The amount earned by the investment is the difference between the future value and the present value.
The future value is determined using the FV formula for continuous compounding.
Principal = $10,000
Interest rate = 20%
Time = 10 years
FV = P * e^rt
P = principal
e = natural log, or 2.7183
r = interest rate
t = time
FV = P * e^rt
= 10,000 x 2.7183^{0.2 x 10}
= 10,000 x 2.7183^2
= 10,000 x 7.389155
= $73,891.55
Amount earned = $63,891.55 ($73,891.55 - $10,000)
Complete Question:
If they invest $10,000 at an interest rate of 20% compounded continuously, how much will the investment earn if it is compounded continuously at the same interest rate for 10 years?