Question

You started saving for a car when you were in middle school. You have done some research and discovered that it will cost you about $8,000 for a used car that would fit your needs. You were encouraged to invest some of your savings to help you get to your financial goal faster. So far you have saved $6,500. If you invest this money in a savings account with a 1.4% interest rate compounded annually, how long will it take to earn enough money to go purchase the car? Use the compound interest formula A = P (1 + i)n, where A is the accumulated amount, P is the principal, i is the interest rate per year, and n is the number of years. Round your final answer to the nearest tenth

Answer 1

Answer: $2,833.47

Explanation:

Part 1:

n = [lnA - lnP] / ln(1 + i)

n = [ln15000 - ln10000] / ln(1 + 0.03)

n = [9.6158 - 9.2103] / 0.0296

n = 13.70

13 years, 8 months, and 12 Days

Part 2:

P = A / [(1 + i)n]

P = 15000 / [(1.03)4]

P = 15000 / 1.1255

P = $13,327.31

Part 3:

A = 10000 (1 + 0.04)5

A = $12,166.53

The amount of money you need to save to buy a car at $15,000 would be;

$15,000 - $12,166.53

=> $2,833.47