Question

Drake wants to deposit $3,600 into an account for 5 years with no additional deposits or withdraws. If there are two options, both offered at 5.2% interest, how much more would be in an account with interest compounded semi-annually versus an account with simple interest?

Answer 1

To find the difference in the final amounts, we calculate the amounts using the formulas for compound interest and simple interest. The account with interest compounded semi-annually will have $74.01 more than the account with simple interest.

Step-by-step explanation:

To calculate the amount in an account with interest compounded semi-annually, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the initial deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = $3,600, r = 5.2% = 0.052, n = 2, and t = 5. Plugging in these values, we find:

A = 3600(1 + 0.052/2)^(2*5) = 3600(1.026)^10 = $4,610.01

To calculate the amount in an account with simple interest, we can use the formula A = P(1 + rt), where A is the final amount, P is the initial deposit, r is the annual interest rate, and t is the number of years. In this case, P = $3,600, r = 5.2% = 0.052, and t = 5. Plugging in these values, we find:

A = 3600(1 + 0.052*5) = 3600(1.26) = $4,536

Therefore, the difference in the final amounts is $4,610.01 - $4,536 = $74.01. So the account with interest compounded semi-annually will have $74.01 more than the account with simple interest.

Answer 2

To calculate the difference between compound interest with semi-annual compounding and simple interest, we can use the formulas for each and compare the final amounts. After performing the calculations, there would be $13.29 more in the account with compound interest compounded semi-annually compared to simple interest.

Step-by-step explanation:

To determine the difference between compound interest and simple interest, we need to calculate the amounts separately. First, let's calculate the amount with simple interest using the formula A = P(1 + rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.

For simple interest, we have: A = 3600(1 + 0.052*5) = 3900. So, with simple interest, there would be $3,900 in the account after 5 years.

Now, let's calculate the amount with compound interest. The formula for compound interest is A = P(1 + r/n)^(nt), where n is the number of times the interest is compounded per year.

For semi-annual compounding, we have: A = 3600(1 + 0.052/2)^(2*5) = 3913.29. So, with compound interest compounded semi-annually, there would be $3,913.29 in the account after 5 years.

The difference between the two amounts is $3913.29 - $3900 = $13.29.

Therefore, there would be $13.29 more in the account with compound interest compounded semi-annually compared to simple interest.