QuestionPS-58 Number of years needed to acccumulate a future amount For each of the following cases, determine the number of years it will take for the initial deposit to grow to equal the furure amount at the given interest rate.
CHAPTER 5 Time Value of Money 295 \begin{tabular}{cccc} Case & Initial deposit & Future amount & Interest rate \\ \hline A & $\$ 300$ & $\$ 1,000$ & $7 \%$ \\ B & 12,000 & 15,000 & 5 \\ C & 9,000 & 20,000 & 10 \\ D & 100 & 500 & 9 \\ E & 7,500 & 30,000 & 15 \end{tabular}

Studdy Solution
Calculate $n$ for each case:
Case A: $$n \approx \frac{\ln(3.3333)}{\ln(1.07)} \approx 18.05$$
Case B: $$n \approx \frac{\ln(1.25)}{\ln(1.05)} \approx 4.56$$
Case C: $$n \approx \frac{\ln(2.2222)}{\ln(1.10)} \approx 8.41$$
Case D: $$n \approx \frac{\ln(5)}{\ln(1.09)} \approx 17.67$$
Case E: $$n \approx \frac{\ln(4)}{\ln(1.15)} \approx 9.67$$
The number of years needed for each case is approximately:
Case A: $18.05$ years \\ Case B: $4.56$ years \\ Case C: $8.41$ years \\ Case D: $17.67$ years \\ Case E: $9.67$ years