AP Business with Personal Finance · Free-response skill

Calculation: save first or borrow now

The move. Set up and carry out saving and borrowing calculations step by step, label each result, and use the numbers to back a recommendation.

How to do it

  1. Write the formula with the numbers in it before you calculate, so a reader can follow every step and give credit for the setup.
  2. Label each answer with what it is and its unit: “total interest: 250 dollars,” not just “250.”
  3. For simple interest, the yearly interest stays the same each year. For compound interest, multiply by (1 + rate) once for each year, so the interest grows.
  4. A recommendation should name the choice and give at least one number from your work that supports it. Mention a trade-off if there is one.

Practice prompt Try it

Dev has 4,000 dollars in savings and wants a fictional used motorcycle that costs 4,400 dollars. He is choosing between two plans. Plan A: wait two years. His savings account pays 5 percent a year, compounded once a year, and he will add nothing more. He expects the motorcycle’s price to stay at 4,400 dollars. Plan B: buy now. He pays 1,000 dollars down from savings and borrows 3,400 dollars at 9 percent APR for 36 months, with a monthly payment of 108.12 dollars.

Use the scenario to respond to each part. Show your work.

  1. Work out how much interest the 4,000 dollars would earn in two years if the account paid 5 percent simple interest instead.
  2. Work out the balance after two years with the account’s real terms: 5 percent compounded once a year.
  3. For Plan B, work out the total of all the loan payments and the total interest Dev would pay.
  4. Recommend Plan A or Plan B. Support your choice with at least one number from your answers, and give one downside of your choice.

Write each part, then check yourself against the checklist. Nothing you type here is saved or graded.

Check yourself and see a model answer

Checklist

Our own checklist of what a full answer does, one line per point. Tick each one your response earns.

0 of 6 points

Model answer, annotated

(a) Simple interest = 4,000 x 0.05 x 2 = 400 dollars.

  • Point 1 Writes the simple-interest formula with the numbers and labels the 400 dollars.

(b) Compound balance = 4,000 x 1.05 x 1.05 = 4,000 x 1.1025 = 4,410 dollars after two years, 10 dollars more than with simple interest.

  • Point 2 Multiplies by 1.05 once per year and gives the balance, 4,410 dollars.

(c) Total of the loan payments = 108.12 x 36 = 3,892.32 dollars. Total interest = 3,892.32 - 3,400 = 492.32 dollars.

  • Point 3 Payment times the number of payments, labeled as the total.
  • Point 4 Subtracts the amount borrowed to isolate the interest.

(d) I recommend Plan A. After two years Dev would have 4,410 dollars, enough for the 4,400 dollar motorcycle, and he would pay no loan interest, while Plan B costs 492.32 dollars in loan interest. The downside is that he must wait two years for the motorcycle, and its price could rise in that time.

  • Point 5 Names Plan A and backs it with 4,410 and 492.32 dollars from the work.
  • Point 6 Gives a real downside of Plan A: the wait and the price risk.