The Weird family wants to buy a small vacation house in a year and a half. They

Question

The Weird family wants to buy a small vacation house in a year and a half. They expect it to cost $75,000 at that time. They have the following sources of money:

1. $10,000 in a bank account that pays 6% compounded monthly.
2. Uncle Murray has promised to give them $1,000 per month, for 18 months, starting today.
3. At the time of purchase they'll take out a mortgage. They anticipate being able to make payments of about $300 a month, on a 15-year loan, at 12%.

In addition, they plan to make quarterly deposits to an investment account to cover any shortfalls in the amount required. How much must those additions be if the investment account pays 8% compounded quarterly?

Explanation / Answer

Let's look at each of the options to see what they will be worth in 18 months: 1) 10,000 currently in the bank account that pays 6% compounded monthly $10,000 X (1.005^18) = $10,939.29 2) Uncle Murray has promised to give them 1,000 a month for 18 months starting today $1,000 X 18 = $18,000 (assumes they just keep the cash on and and not in an interest bearing bank account - since the problem doesn't tell us that they invested these funds, I assumed that they didn't.) 3) At the time of purchase they take out a mortgage and they anticipate being able to make payments of about 300 a month on a 15 year , 12 % loan. The Present Value of this loan = $24,996.50 (Number of Periods = 180, Interest Rate = 1% (12%/12), Monthly Payment = $300) The remaining amount they will need to get from the additional investment is ($75,000 - $10,939.29 - $18,000 - $24,996.50 =) $21,064.21. To get $21,064.21 in 6 quarters (18 months) using an investment that pays 8%, compounded quarterly, they need to put $3,339.22 in the account every quarter. This was calculated using the PMT (Payment) function in Excel, with (Interest Rate = 8%/4, Number of Periods = 6 (18 months / 3), Future Value = $21,064.21) The answer came back as $3,339.22 You can also use a Financial calculator that computes Present Value formulas. I have a HP12C calculator and double checked all the calculations on it. All the numbers agreed with the values calculated in Excel.

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