Question

2. Ben is making two separate investments with his $2,400

inheritance.
He will invest $1,500 in Investment R which pays 2.75%
annual simple interest
He will invest $900 in Investment S which pays 2.75%
interest compounded annually
a. What is the difference between the balance of the two
investments after 8 years?
b. What is the difference between the interest earned of the two
investments after 8 years?
c. Which of the two had the better return on investment?

Answer 1

Explanation:

We can use the simple interest formula:

R = P(1 + rt)

where R is the balance, P is the principal, r is the interest rate, and t is the time.

For Investment R, we have:

R = 1,500(1 + 0.0275*8)

R = 1,980

For Investment S, we can use the formula:

R = P(1 + r)^t

R = 900(1 + 0.0275)^8

R = 1,116.92

a. The difference between the balance of the two investments after 8 years is:

1,980 - 1,116.92 = 863.08

b. The interest earned for Investment R is:

I = Prt

I = 1,500*0.0275*8

I = 330

For Investment S, we can calculate the interest using:

I = R - P

I = 1,116.92 - 900

I = 216.92

The difference between the interest earned on the two investments is:

330 - 216.92 = 113.08

c. To compare the return on investment, we can use the concept of compound interest.

For Investment R, the total value after 8 years is:

R = 1,500(1 + 0.0275*8)

R = 1,980

For Investment S, we can calculate the effective annual rate:

EAR = (1 + r/n)^n - 1

EAR = (1 + 0.0275/1)^1 - 1

EAR = 0.0275

The total value after 8 years is:

R = 900(1 + 0.0275)^8

R = 1,116.92

The return on investment for Investment R is:

ROI = (1 + r/n)^nt - 1

ROI = (1 + 0.0275/1)^1*8 - 1

ROI = 0.2229

The return on investment for Investment S is:

ROI = (1 + EAR)^t - 1

ROI = (1 + 0.0275)^8 - 1

ROI = 0.2329

Therefore, Investment S had the better return on investment.