Question
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.
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.
Answers
Answered by
GPT 3.5
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.
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.