Question

Your flight and hotel stay total $2,500, and you figure by the time you add in all of the extra side trips, tickets, meals, and foam fingers you buy at the baseball game, you’re in for at least another $1,000, bringing your vacation budget to $3,500.

However, this isn’t “The Price Is Right” (more on that later) and you have saved up $3,000 in your vacation budget to enjoy this somewhat lavish trip to one of the oldest cities in the US. You have decided that since you are close, you are going to evaluate your options for financing this trip.

Now, you will investigate your options for paying for the remaining $500. Here are your options (some involve patience, some involve going now…) – assume all rates that are quoted are annual rates, so be careful on setting up your formulas.

1. You decide to put your money in a simple interest account, planning to let your $3,000 grow into $3,500 so you can take the trip. What interest rate do you need on your account to get your money in 2 years?

2. Your bank offers you a unique one-time deal – they will pay you 8% compounded monthly. How many months will it take for you to earn enough interest to get to $3,500?

3. You decide to explore one other option that takes time – opening another account that pays 4% interest, compounded monthly. If you make regular payments to this account, how much will you have after one year (pro tip: use the sinking fund formula)?

4. Another option is to take out an unsecured installment loan from your bank; this will let you borrow the $500 over the course of one year, but the bank requires monthly payments and the interest rate on your loan is 10%. How much are your regular payments?

5. You’ve booked your trip and saved your money, but just a few days before you are to depart on your vacation, the water pump goes out on your car and it’s a $450 repair bill that you weren’t counting on. You have to put this on a credit card that has an interest rate of 15%, but when you come back, because of the vacation, you can only make $50 payments each month until it’s paid off. How long will it take you to pay off the credit card debt?

Answer 1

Question 1 Computation of simple interest rate Maturity value 3,500 Principle amount 3,000 Total Interest 500 Period 2 years Simple Interest rate p.a 8.33% (500/3000)/2 Question 2 Computation of no. of months Maturity Value (mv) 3,500 Principle amount (P) 3,000 Monthly rate of interest (r) (8%/12) 0.67% Hence, P(1+r)An = mv 3000* (1+0.0067)^n 3500 (1.0067)^n 3500/3000 (1.0067)An 1.1667 n 23.20 months (Computed using log formula) Question 3 Computation of Future Value Money in hand 3,000 $ Monthly payment for a year (3000/12) FV Annuity (4% p.a, 12 M) 250 12.2225 $3,055.63 Future Value (250*12.2225)

Question 4 Computation monthly installment Borrowing 3000 PV Annuity (10% p.a, 12 months) 11.3745 Monthly installment (3000/11.3745) $263.75 Question 5 Computation no. of months $ Principle (P) 450 Monthly installment (m) Monthly rate of interest (r) (15%/12) 50 1.25% This could be solved by interpolation method no. of months be 9, P will be Assuming no. of months be 10, P will be Assuming m* PVAF(1.25%, 9 months) m* PVAF(1.25%, 10 months) 50*8.4623 50*9.3455 423.115 467.28 Hence, n 9 (450-423.115)/(467.26-423.115) n 9.61 months