Answer:
The correct option is;
(f) 7.6%
Step-by-step explanation:
The given parameters are;
The number of years Tom and Jerry are investing their money, t = 8 years
The rate of return for Tom's investment, r₁ = 9%
The rate of return for Jerry's investment, r₂ = 10%
The rate at which the interest is compounded, n = Annually = 1
Let P represent the equal amount of money each of Tom and Jerry invested separately
The amount, A, of the investment is given by the following formula;
![A = P \times \left (1 + \dfrac{r}{n} \right ) ^{n \times t}](https://tex.z-dn.net/?f=A%20%3D%20P%20%5Ctimes%20%5Cleft%20%281%20%2B%20%5Cdfrac%7Br%7D%7Bn%7D%20%5Cright%20%29%20%5E%7Bn%20%5Ctimes%20t%7D)
Substituting the known values for Tom, gives;
![A = P \times \left (1 + \dfrac{0.09}{1} \right ) ^{1 \times 8} = P \times 1.09^8 \approx 1.993\cdot P](https://tex.z-dn.net/?f=A%20%3D%20P%20%5Ctimes%20%5Cleft%20%281%20%2B%20%5Cdfrac%7B0.09%7D%7B1%7D%20%5Cright%20%29%20%5E%7B1%20%5Ctimes%208%7D%20%3D%20P%20%5Ctimes%201.09%5E8%20%5Capprox%201.993%5Ccdot%20P)
The amount Tom has after 8 years ≈ 1.993·P
Substituting the known values for Jerry, gives;
![A = P \times \left (1 + \dfrac{0.1}{1} \right ) ^{1 \times 8} = P \times 1.1^8 \approx 2.144\cdot P](https://tex.z-dn.net/?f=A%20%3D%20P%20%5Ctimes%20%5Cleft%20%281%20%2B%20%5Cdfrac%7B0.1%7D%7B1%7D%20%5Cright%20%29%20%5E%7B1%20%5Ctimes%208%7D%20%3D%20P%20%5Ctimes%201.1%5E8%20%5Capprox%202.144%5Ccdot%20P)
The amount Jerry has after 8 years ≈ 2.144·P
The percentage amount Jerry has more than Tom after 8 years, PA is given as follows;
The amount Jerry will have after 8 years than Tom = PA ≈ 7.6%.