Question

1. Gloria wants to have $20,000 in 5 years for a house down payment. What single deposit would she need to make now into an account that pays 2.6% interest, compounded daily, to meet her goal? Round to the nearest dollar.

2. Karen opens an account at the local bank by depositing $25 of her birthday money. She continues to deposit $25 each week for 3 years. If the account pays 2.25% interest compounded weekly, how much is in the account after 3 years? Round to the nearest cent.

3. Mark sold his car for $16,500. He placed half of the money into a account with a 2.75% interest rate compounded daily. He placed the other half into a different account with the same interest rate which is compounded monthly. What is the difference in the interest earned on each amount after 5 years? Round to the nearest cent.

4. Tom and Loren are saving for retirement. Their goal is to have $450,000 in 35 years. They open up an account that pays 4.2% interest compounded monthly. How much should they deposit each month to meet their goal? Round to the nearest dollar.

5.
Sam wants to go on a $5,000 vacation in 9 months. He has a bank account that pays 4.0%, compounded monthly. How much must he deposit today to afford the vacation? Round to the nearest cent.

Answer 1

Answer: Karen opens an account at the local bank by depositing $25 of her birthday money. She continues to deposit $25 each week for 3 years. If the account pays 2.25% interest compounded weekly, how much is in the account after 3 years? Round to the nearest cent.

Explanation:

To determine the single deposit Gloria would need to make now, we can use the formula for compound interest :A = P(1 + r/n)^(nt) Where:A = the final amount (in this case, $20,000)P = the principal (the initial deposit we are trying to find)r = the annual interest rate (2.6% or 0.026)n = the number of times interest is compounded per year (365, since it is compounded daily)t = the number of years (5)Plugging in these values, we have:$20,000 = P(1 + 0.026/365)^(365*5)Now, solve for P to find the initial deposit Gloria would need to make.2. Karen opens an account by depositing $25 initially and then $25 each week for 3 years. To calculate the final amount in the account, we can use the formula for compound interest again:A = P(1 + r/n)^(nt)Where:A = the final amount in the accountP = the principal (initial deposit)r = the annual interest rate (2.25% or 0.0225)n = the number of times interest is compounded per year (52, since it is compounded weekly)t = the number of years (3)Using these values, we can calculate the final amount in the account after 3 years.