Subjects finance

Annuity Deposit D49Ca3

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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.