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 amount of money earned with each option after 4 years.
For the 8.3% simple interest rate, the formula to calculate the final amount (A) after a given period of time (t) is:
A = P(1 + rt)
where P is the principal amount, r is the interest rate, and t is the time in years.
Using this formula, the amount earned with an 8.3% simple interest rate after 4 years is:
A = 3800(1 + 0.083*4)
A = 3800(1 + 0.332)
A = 3800(1.332)
A = $5,059.60
For the 7.2% compound interest rate compounded monthly, the formula to calculate the final amount (A) after a given period of time (t) is:
A = P(1 + r/n)^(nt)
where P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Using this formula, the amount earned with a 7.2% compound interest rate after 4 years is:
A = 3800(1 + 0.072/12)^(12*4)
A = 3800(1 + 0.006)^(48)
A = 3800(1.006)^(48)
A = $5,073.97
Comparing the two amounts, we can see that $5,073.97 earned with the 7.2% compound interest rate is greater than $5,059.60 earned with the 8.3% simple interest rate.
Therefore, the better investing option is the 7.2% compound interest rate with interest compounded monthly, so the answer is 2.