Question: 1. A new setup company estimates it will have to replace one of its delivery trucks s five years from now. The replacement is estimated to cost not less than $160,000 which it plans to finance by depositing an equal amount at Ecobank at the end of each month into an account with a return of 0.90% per month. What is the amount to be deposited each month in order to realize the required amount?
1. **State the problem:**
A company needs to accumulate at least $160000$ in 5 years by making equal monthly deposits into an account that earns $0.90\%$ interest per month. We need to find the monthly deposit amount.
2. **Formula used:**
We use the future value of an ordinary annuity formula:
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where:
- $FV$ is the future value ($160000$),
- $P$ is the monthly deposit (unknown),
- $r$ is the monthly interest rate ($0.009$),
- $n$ is the total number of deposits ($5 \times 12 = 60$).
3. **Substitute known values:**
$$160000 = P \times \frac{(1 + 0.009)^{60} - 1}{0.009}$$
4. **Calculate $(1 + 0.009)^{60}$:**
$$ (1.009)^{60} \approx 1.689478$$
5. **Calculate numerator:**
$$1.689478 - 1 = 0.689478$$
6. **Calculate fraction:**
$$\frac{0.689478}{0.009} \approx 76.6087$$
7. **Solve for $P$:**
$$160000 = P \times 76.6087$$
$$P = \frac{160000}{76.6087}$$
8. **Simplify fraction with cancellation:**
$$P = \frac{\cancel{160000}}{\cancel{76.6087}} \approx 2089.07$$
9. **Final answer:**
The company must deposit approximately **$2089.07$** at the end of each month to accumulate $160000$ in 5 years.