Question

You need a down payment of $17,200 in order to purchase your first home 4 years from today. You currently have $14,014 to invest. In order to achieve your goal, what nominal interest rate, compounded continuously, must you earn on this investment

Answer 1

Answer:Interest rate must be R = 6.04%

Explanation:

When an investment earns interest compounded continuously it means interest is earned constantly, Compound interest is usually calculated on monthly, quarterly semi annual and annual intervals. Continuous compounding is theoretical concept which aims to calculate interest at the smallest possible interval.

Future Value = $17200

Present Value = $14014

n = 4

Future Value = Present Value x e^rn

$17200 = $14014 x e^(r x 4)

e^(r x 4) = 17200/14014

e^(r x 4) = 1.2273440845

e = 2.7182818285

(2.7182818285)^(r x 4) = 1.2273440845

(r x 4)log(2.7182818285) = log(1.273440845)

r x 4 =  log(1.273440845)/log(2.7182818285)

r x 4 = 0.2417225636

r = 0.2417225636/4 = 0.0604306409

R = 6.04%