Question

You currently have $3,400 in an investment account that returns 11% per year. How long will you have to wait until you can make $5,000 down payment on a car?A loan you took out is due in three years and requires repayment of $3000. To pay off the loan, you set aside money in an account that pays 7% interest. In order to meet your obligation, how much money needs to be in the account now?

Answer 1

Answer:

1) 3.7 years

2) $2,448.89

Explanation:

1. Amount in bank  = $3,400

Return, r = 11% = 0.11

Future value = $5,000

Now,

Future value = Principle × ( 1 + r )ⁿ

here,

n is the time

$5,000 = $3,400 × ( 1 + 0.11 )ⁿ

or

1.4706 = 1.11ⁿ

taking log both sides

log(1.4706) = log(1.11ⁿ)

also,

log(aᵇ) = b × log(a)

Thus,

log(1.4706) = n × log(1.11)

0.1675 = n × 0.0453

or

n = 3.69 ≈ 3.7 years

2) Amount to repay = $3,000

Interest = 7% = 0.07

Time, n = 3 years

Now,

Future value = Principle × ( 1 + r )ⁿ

or

$3,000 = Principle × ( 1 + 0.07 )³

or

$3,000 = Principle × 1.225043

or

Principle = $2,448.89

Hence,

Amount to be set aside = $2,448.89