Question

You want to buy your dream car which will cost you $5900. If you could invest your entire savings of $3500 at an annual interest of12%, how long (in years rounded to two decimal places) would you have to wait until you have accumulated enough money to buy the car?

Answer 1

To accumulate enough money to buy the car, it would take approximately 6.84 years (rounded to two decimal places).

Step-by-step explanation:

To calculate the time it will take to accumulate enough money to buy the car, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the accumulated amount

P is the principal (initial savings)

r is the annual interest rate (as a decimal)

n is the number of times interest is compounded per year

t is the number of years

In this case:

P = $3500

r = 0.12

n = 1 (since interest is compounded annually)

A = $5900

Substituting these values into the formula, we can solve for t:

$5900 = $3500(1 + 0.12/1)^(1t)

$5900/$3500 = 1.12^t

1.6857 ≈ 1.12^t

t ≈ log(1.6857) / log(1.12)

t ≈ 6.84

Therefore, it would take approximately 6.84 years (rounded to two decimal places) to accumulate enough money to buy the car.