Adam wants to invest $80,000 in a pension plan. One investment offers 7% compounded quarterly. Another offers 6.5% compounded continuously. Which investment will earn more interest in 10 years?
compare
(1+.07/4)^4
and
e^0.065
That gives the interest in one year. The greater here will also be greater in 10 years.
To determine which investment will earn more interest in 10 years, we can compare the future values of the two investments using the compound interest formula:
Future Value = Principal * (1 + (rate / n))^(n * t)
Where:
- Principal is the initial investment amount
- Rate is the interest rate as a decimal
- n is the number of compounding periods per year
- t is the number of years
Let's calculate the future values for both investments and compare them:
For the first investment with a rate of 7% compounded quarterly:
Principal = $80,000
Rate = 7% = 0.07
n = 4 (quarterly compounding)
t = 10 years
Future Value = $80,000 * (1 + (0.07 / 4))^(4 * 10) = $172,329.75
For the second investment with a rate of 6.5% compounded continuously:
Principal = $80,000
Rate = 6.5% = 0.065
n = ∞ (continuous compounding)
t = 10 years
Future Value = $80,000 * e^(0.065 * 10) = $178,008.92
Comparing the future values, we see that the investment with 6.5% compounded continuously will earn more interest in 10 years. It will have a future value of $178,008.92, whereas the investment with 7% compounded quarterly will have a future value of $172,329.75.