Final answer:
Jerome would earn more total interest with the investment plan of 3.7% interest compounded continuously, resulting in $55397.32 of total interest, compared to $32640 earned through 5.1% simple interest over 32 years.
Step-by-step explanation:
When comparing the two investment options for Jerome, we will calculate the total interest earned for both the simple interest account and the account with interest compounded continuously.
Simple Interest Calculation
Simple interest is calculated using the formula:
I = Prt
Where:
I = interest,
P = principal amount ($20,000),
r = annual interest rate (5.1% or 0.051),
t = time in years (32).
So, I = 20000 * 0.051 * 32 = $32640
Continuous Compound Interest Calculation
Interest compounded continuously is calculated using the formula:
A = Pert
Where:
A = amount after t years,
P = principal amount ($20,000),
r = annual interest rate (3.7% or 0.037),
t = time in years (32),
e = base of the natural logarithm.
So, A = 20000 * e(0.037*32) = 20000 * e1.184 = $75397.32
Therefore, the total compound interest would be $75397.32 - $20000 = $55397.32
Comparing the two total interests:
- Simple interest: $32640
- Compound interest: $55397.32
Jerome would earn more total interest with the 3.7% interest compounded continuously.