Personal Finance Math Problems and Interest Calculations

Personal Finance Math and Interest Calculations

Interest and Yield Calculations

1. Simple Interest: Katie invests $2,300 in an account that pays 7% simple interest annually. Find the future value of the account after 9 years. Round your answer to the nearest cent.
2. Monthly Compounding: Suppose you invest $1,900 at a fixed rate of 5% per year, compounded monthly. Find the future value of the account after 6 years. Round your answer to the nearest cent.
3. Continuous Compounding: Suppose you instead invest your $1,900 in an account that earns 6% interest compounded continuously. What is the total amount of your investment after 7 years? Round your answer to the nearest cent.
4. Effective Annual Yield: Find the effective annual yield to the nearest hundredth of a percent for an account paying 4% compounded quarterly.
5. Credit Card Interest: Sean’s Visa card statement shows an average daily balance of $712 for the month. Find the interest due this month if the annual percentage rate is 15.99%.

Loans, Mortgages, and Investments

6. Installment Loans: Jaron buys a new TV for $1,400 using in-store financing. He makes a $300 down payment for the TV. The store charges add-on interest of 4.5% per year, and Jaron agrees to pay the loan with 24 equal monthly payments.
   • a. Find the total amount of interest he will pay.
   • b. Find the monthly payment.
7. Actuarial Method: Suppose Jaron decides to pay off the loan with 6 months remaining. The finance charge per $100 for this loan with 6 months remaining is $1.32. Use the actuarial method to find the following:
   • a. Find the unearned interest.
   • b. Find the payoff amount.
8. Mortgage Calculations: A home is purchased using a loan for $351,000. The loan is a 35-year fixed mortgage at 7% interest. Annual property taxes are $3,100 and annual insurance is $1,700. For this home, calculate the following:
   • a. The monthly payment for principal and interest for the loan.
   • b. Find the total monthly payment including taxes and insurance.
   • c. Find how much interest will be paid over the life of the loan.
   • d. If the lender charges one point, how much does that add to the cost of the loan?
9. Mutual Funds: A mutual fund has $1.4 billion in assets, $200 million in liabilities, and 13 million shares outstanding.
   • a. Find the net asset value of the mutual fund.
   • b. How many shares can be purchased for $51,000?
10. Retirement Planning: Ann decides to contribute $8,500 at the end of each year to a retirement account. The account earns a 9% annual return, and Ann’s marginal tax rate is 34%. She plans to retire in 35 years.
    • a. Find the amount of money in the account at the end of 35 years if the account is a tax-deferred account.
    • b. Find the amount of money in the account at the end of 35 years if the account is a taxable account.
    • c. Which account type should she invest her money in? Justify your answer.