Question

Neil and John both need $20,000 to clear off a mortgage payment after 10 years. Neil invests $15,000 at 3 percent per annum of simple interest for 10 years, and John invests $15,000 at 3 percent compound interest compounded annually for 10 years. Who would be able to repay the amount from this investment easily?

Answer 1

John will be able to repay the amount from this investment easier than Neil.

Because Neil has invested in simple interest, his amount at the end of 10 years will be equal to the interest earned and the principal amount.

According to the problem:

P (principal) = $15,000, I = 3%=0.03 and t =10 years

Therefore, I = P x r x t = 15,000 x 0.03 x 10 = $4,500

The amount at the end of 10 years

= principal + interest

= 15,000 + 4,500

= $19,500

On the other hand, John has invested his $15,000 in 3 percent compound interest compounded annually for 10 years.

According to the problem: P

= $15,000

I

= 3% = 0.03

n

= 10

Therefore, according to the formula

M = P( 1 + i )n where M is the final amount at the end of the term, we have

M = 15,000(1+0.03)10

= 20,158.75 (approximately).

= $20,158.75

Therefore, John will be able to repay the debt from this investment easily, because Neil is $500 short of the required amount.

Answer 2

John

Step-by-step explanation:

Neil will have the following amount after ten years.

Simple interest is calculated using the formula,

I= p x r x t

where I= interest, P= principal amount, r = interest rate, t is time

for Neil interest will be= $15,000 x 3/100 x 10

=$15,000 x 0.03 x 10

=$4500

Neil will have principal + interest amount

=$4,500 + $15,000

=$19,500

John invested in a compound interest account.

The amount after ten years will be

The formula for compound interest is

FV = PV × (1+r)^n

where FV = Future Value

PV = Present Value

r = annual interest rate

n = number of periods

After ten years, John will have

Fv= $15,000 x (1 + 3/100)^10

Fv= $15,000 x (1.03)^10

FV =$15,000 x 1.34391

Fv = $15,158.75

John will be able to clear his mortgage.