Determine whether an 8.3% simple interest rate or a 7.2% compound interest rate with interest compounded monthly is the better
investing option when $3,800 is invested for 4 years. Enter 1 if an 8.3% simple interest rate is the better option.
Enter 2 if a 7.2% compound interest rate with interest compounded monthly is the better option.
To compare the two options, we need to calculate the final amount for each option and compare them.
For a simple interest rate:
Interest = Principal * Rate * Time
Interest = 3800 * 0.083 * 4 = $1260.80
Final amount = Principal + Interest = 3800 + 1260.80 = $5060.80
For a compound interest rate with interest compounded monthly:
Formula for compound interest is:
A = P (1 + r/n)^(nt)
Where:
A = final amount
P = principal amount
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
For this case:
Principal = $3800
Rate = 7.2% = 0.072 (as a decimal)
Time = 4 years
n = 12 (compounded monthly)
A = 3800 (1 + 0.072/12)^(12*4)
A ≈ 3800 * 1.017^48
A ≈ 3800 * 1.366732856 ≈ $5190.56
Comparing the final amounts:
For a simple interest rate, the final amount is $5060.80
For a compound interest rate, the final amount is $5190.56
Since $5190.56 is greater than $5060.80, a 7.2% compound interest rate with interest compounded monthly is the better option. Therefore, the answer is 2.