Name Date MAT 1460 Homework Section 53 Support your answer b

Name: Date: MAT 1460- Homework Section 5.3 Support your answer by showing your work. Sylvia is planning to deposit $100 at the end of each month into her daughter\'s college fund. If the account pays 3.6% annual interest compounded monthly, how much will be in the account in 15 years? How much of that will be interest? Round both answers to the nearest cent. 1. A company needs to set up a sinking fund to pay off a $1,000,000 lawsuit in 5 years. Assuming that the fund earns 6% annual interest compounded quarterly, what should be the end of the quarter payments? Round your answer to the nearest dollar. 2. 3. Jennifer is able to invest $50 at the beginning of each month towards a car in 5 years. If the account pays 4.2% annual interest compounded monthly. How much will be in the account? How much of that was interest? Round your answers to the nearest cent

Solution

Answer to Question 1:

Monthly Saving = $100
Annual Interest Rate = 3.60%
Monthly Interest Rate = 0.30%
Period = 15 years or 180 months

Accumulated Sum = $100*1.003^179 + $100*1.003^178 + $100*1.003^177 + ... + $100*1.003 + $100
Accumulated Sum = $100 * (1.003^180 - 1) / 0.003
Accumulated Sum = $100 * 238.2067
Accumulated Sum = $23,820.67

Total Deposit made = 180 * $100
Total Deposit made = $18,000

Total Interest = Accumulated Sum - Total Deposit made
Total Interest = $23,820.67 - $18,000
Total Interest = $5,820.67