Question

Karl Yates needs ​$24,000 to pay for the remodeling work on his house. A contractor agrees to do the work in 10 months. How much should Karl deposit at 7.4​% in order to accumulate the ​$24,000 by that​ time?

Answer 1

Answer:

$22614 needs to be deposited today.

Explanation:

Let x be the amount we will initially invest. The investment will be made for 10 months while the interest rate given here as 7.4% is the annual interest rate.

So,

• 24000 = x * ( 1 + 0.074 )^10/12

• 24000 / ( 1 + 0.074)^10/12 = x

• x = $22613.84 rounded off to $22614

Thus if Karl makes an initial investment of $22614  at 7.4% annual interest rate, then he will be able to withdraw a combined Principal + Interest of $24000 after 10 months.