Question

Jerome wants to invest $20,000 as part of his retirement plan. He can invest the money at 5.1% simple interest for 32 yr, or he can invest at 3.7% interest compounded continuously for 32yr. Which investment plan results in more total interest? 3.7% interest compounded continuously 5.1% simple interest

Answer 1

The compound interest plan results in more total interest, earning $298.86 more than the simple interest plan.

Step-by-step explanation:

To determine which investment plan results in more total interest, we need to calculate the interest earned for each plan.

For the simple interest plan, we can calculate the total interest using the formula:

Interest = Principal x Rate x Time

So for the simple interest plan, the total interest earned would be:

Interest = $20,000 x 0.051 x 32 = $32,640

For the compound interest plan, we can use the formula:

Final Amount = Principal x e^(Rate x Time)

So for the compound interest plan, the total interest earned would be:

Interest = Final Amount - Principal = $20,000 x (e^(0.037 x 32) - 1) = $32,938.86

Therefore, the compound interest plan results in more total interest. The difference is $32,938.86 - $32,640 = $298.86.

Answer 2

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.