1. **State the problem:** A couple wants to save N1.5 million in 5 years by making equal yearly deposits into an annuity account with an annual interest rate of 17%, compounded annually.
2. **Formula used:** The future value of an ordinary annuity is given by
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where $FV$ is the future value, $P$ is the yearly deposit, $r$ is the annual interest rate (as a decimal), and $n$ is the number of years.
3. **Given values:**
- $FV = 1,500,000$
- $r = 0.17$
- $n = 5$
4. **Rearrange the formula to solve for $P$:**
$$P = \frac{FV \times r}{(1 + r)^n - 1}$$
5. **Calculate the denominator:**
$$(1 + 0.17)^5 - 1 = 1.17^5 - 1$$
Calculate $1.17^5$:
$$1.17^5 = 1.17 \times 1.17 \times 1.17 \times 1.17 \times 1.17 = 2.1927$$
So,
$$2.1927 - 1 = 1.1927$$
6. **Calculate $P$:**
$$P = \frac{1,500,000 \times 0.17}{1.1927} = \frac{255,000}{1.1927}$$
7. **Simplify the fraction:**
$$P = 213,774.68$$
**Final answer:** The couple must deposit approximately **213,775** naira yearly to have 1.5 million naira in 5 years.
Annuity Deposit D49Ca3
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