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### 13. Mr. Jonel's Deposit Problem:
We need to calculate the future value of three deposits: P12,000 (now), P8,000 (after two years), and P10,000 (after five years) at a 5% interest rate. This uses the **future value formula for compound interest**:

\[
FV = P(1 + r)^t
\]

We'll calculate the future value for each amount separately and sum them up to find the total future value.

### 14. Diesel Generator Payment:
A factory operator needs to pay a uniform annual sum for five years to clear a debt of P10,000 with 8% annual interest. This problem involves finding the **annuity payment (A)** that will cover both the principal and the interest. The formula for annuity payments is:

\[
A = \frac{P \cdot r}{1 - (1 + r)^{-n}}
\]
Where \(P\) is the principal, \(r\) is the interest rate per period, and \(n\) is the number of periods.

### 15. Annuity Problem:
We need to find the annuity payment required over 12 years to equate to a future amount of P20,000 at a 6% interest rate. This can be calculated using the **present value of an annuity** formula.

### 16. Lot Purchase:
This question asks for the present value of an investment involving a down payment of P100,000 and 10 semi-annual payments of P8,000 each. The interest rate is 12% compounded semi-annually. We will use the **present value of deferred payments** formula.

### 17. Bond Rate of Interest:
This asks for the interest rate on a bond issued at 95% of its face value, with a 3% coupon rate over 15 years. We calculate this using the **yield to maturity** formula, which accounts for both the discount and the coupon payments.

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### 5 Related Questions:
1. How do you calculate future value with multiple deposits?
2. What is the formula for calculating annuity payments?
3. How does compound interest affect semi-annual payments?
4. What are the steps to calculate the yield to maturity for a bond?
5. How can you solve for uniform payments in a loan repayment scenario?

### Tip:
For compound interest problems, always ensure that the interest rate and time periods match the compounding frequency (e.g., annual, semi-annual, monthly) to avoid miscalculations.

13. Mr. Jonel deposits P12,000 now, P8,000 two years from now and P10,000 five years from now. If the savings bank's rate of interest is 5%, he will receive an amount of X, 10 years from now, where 'X' is ___. 14. A factory operator bought a diesel generator set for P 10,000.00 and agreed to pay the dealer uniform sum at the end of each year for 5 years at 8% interest compounded annually, that the final payment will cancel the debt for principal and interest. What is the annual payment? 15. What annuity is required over 12 years to equate with a future amount of P20,000? Assume i= 6% annually. 16. A person buys a piece of lot for P100,000 down payment and 10 deferred semi-annual payments of P8,000 each, starting three years from now. What is the present value of the investment if the rate of interest is 12% compounded semi-annually? 17. A P1,000,000 issue of 3%, 15-year bond was sold at 95%. What is the rate of interest of this investment?

Solve problems related to compound interest, annuity payments, present value of deferred payments, and bond yield to maturity. These problems involve key formulas such as future value, annuity payment calculations, and yield to maturity. Suitable for advanced students.

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