Question

Maribel Salazar has a stock broker account at Diversified Investors Group on which she earns 4.5% interest annually. She buys a car with a loan. The interest rate on the loan is 16.5%, but she doesn't have to make any payments during the first year. Then she will make monthly payments until the loan is paid off. Today, Maribel has: a stock broker account with $11,000, which earns 4.5% interest annually $8000 in car loan debt, with no payments the first year, but with the loan amount increasing by 16.5% at the end of the first year Today, the combined ("net") value of these two accounts is $3000, which is the difference between the value of the stock broker account and the car loan debt (= $11,000 - $8000).

Question 1: According to the terms of her loan, Maribel makes no payments on her car loan for the first year. She also makes no deposits or withdrawals from her stock broker account. At the end of the year, what will be the net value of the two accounts: $ __________

Question 2: If, instead of getting a loan, Maribel bought the car by using money from her stock broker account at the beginning of this year, what would the net value of the two accounts be at the end of the year: $________

Answer 1

Answer 1:

At the start of the year (today):

Car loan debt = $8,000 and rate of interest on it = 16.5% (monthly payments after 1 year)

Stock broker account balance = $11,000 and it earns 4.5% interest annually

Maribel makes no payments on her car loan for the first year. She also makes no deposits or withdrawals from her stock broker account.

At the end of the year:

Loan amount including interest = 8000 * (1 + 16.5%/12) ¹² = $9424.55

Stock broker account balance = 11000 * (1 + 4.5%) = $11,495

Net value of the two accounts = 11495 - 9424.55 = $2,070.45

Net value of the two accounts = $2,070.45

Answer 2:

Maribel bought the car by using money from her stock broker account at the beginning of this year.

In this case:

Balance at Stock broker account at the beginning of this year after payment for the car = 11000 - 8000 = $3,000

Balance at Stock broker account at the end of the year = 3000 * (1 + 4.5%) = $3,135

There would not any loan balance at the end of the year

Net value of the two accounts be at the end of the year = $3135 - $0 = $3,135

Net value of the two accounts be at the end of the year = $3,135