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.