Question

1. Peggy and John Schultz bought the house of their dreams seven years ago. The price was $475,000, though they negotiated it down to a more agreeable $449,500. They paid 20% of that in cash, as a down payment and financed the rest using a 25-year, 4.15% mortgage. Peggy was doing bills the other day and decided to figure out just how much their monthly payment was and how much interest they had paid thus far. She also wants to calculate the amount of principle they have paid and what the remaining balance that they still owe on their mortgage is currently. Can you help her with these figures?

2. Clarence Beeks contributes $5,500 each year to his IRA and has been doing so at the beginning of every year for the past 10 years. His IRA earns an average of 9% each year. It is Clarence’s wish to accumulate $1,250,000 so that he can retire. How many more years will it take for Clarence to accumulate $1,250,000 total assuming he continues to contribute at the same level each year and that his returns stay the same?

3. Jane and John Smith have accumulated $650,000 for their retirement, which begins today. They plan to receive monthly payments from their investments, which will be paid at the beginning of each month over the next 35 years based on their estimated life expectancy. If investments are accumulating at an after-tax annual rate of 5.75%, compounded monthly, what will be the payment amount that the Smiths will receive each month to the nearest dollar?

4. At the end of each year for the first 5 years, Cecil and Norma DeMille plan to contribute $1,000 to their daughter Sally's college fund. For the next 5 years they will contribute $2,000 at the end of each year, and then increase that amount to $3,000 until she turns 18 and is ready for college. What amount will they have accumulated for Sally's college fund if the account pays 6.35% annually?

5. Fred Buffett (Warren's younger brother) started his account with the investment of an inheritance from his grandmother of $16,250, it was generating 4.75% per year, compounded annually. That was over 12 years ago, but today he found an equally safe account (with a tip from his cousin Jimmy Buffett) where he will more than double his interest rate to 9.65% per year. Fred pulled all his money out of the old account and placed it in this new account. He plans to leave the funds alone for another 20 years, at which time he plans to go on a dream cruise. At that time, how much should Fred expect to have in the account?

Answer 1

(1) Original Purchase Price = $ 449500, Cash Down Payment = 20 % of Original Purchase Price = 0.2 x 449500 = $ 89900

Mortgage Amount = 449500 - 89900 = $ 359600

Mortgage Tenure = 25 years, Remaining Mortgage Tenure = (25 - 7) = 18 years and Mortgage Rate = 4.15 %

Monthly Rate = (4.15/12) = 0.34583 %

Let the monthly repayments be $ P

Therefore, 359600 = P x (1/0.0034583) x [1-{1/(1.0034583)^(300)}]

359600 = P x 186.5142

P = 359600 / 186.5142 = $ 1928.0027 ~ $ 1928

After 7 years (at current time) the remaining mortgage should equal the total present value of the remaining monthly payments discounted at the monthly rate.

Therefore, Remaining Mortgage = 1928 x (1/0.0034583) x [1-{1/(1.0034583)^(216)}] = $ 293021.98

Principal Repaid = Original Mortgage - Remaining Mortgage = 359600 - 293021.98 = $ 66578.02

Interest Repaid = Total Monthly Repayments Made - Principal Repaid = [1928 x (300 - 216)] - 66578.02 = $ 95373.98

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