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The image shows two mathematical finance problems from a post-test. I'll summarize and help you with both questions:

### Problem 1
> **Context**: A student wants to save for college education and wishes to accumulate PHP 500,000 in 5 years.
> 
> **Question**: If they save an equal amount every month in an account with a 1.4% interest rate compounded monthly, what should the monthly deposit be?

This is an annuity problem where we calculate the regular monthly deposit needed to reach a future amount with compounding interest.

### Solution Approach for Problem 1:
For a future amount \( FV \) with regular payments (annuity), the formula is:
\[
PMT = \frac{FV \cdot \left( \frac{i}{(1+i)^n - 1} \right)}{1}
\]
where:
- \( PMT \) is the monthly deposit,
- \( FV = 500,000 \) PHP,
- \( i \) is the monthly interest rate (1.4% annually, so \( i = \frac{1.4\%}{12} = \frac{0.014}{12} \)),
- \( n \) is the total number of deposits (5 years \(\times\) 12 months).

Would you like me to calculate the exact monthly deposit?

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### Problem 2
> **Context**: A refrigerator is available either for PHP 17,999 in cash or for PHP 1,600 per month over the next 12 months.
> 
> **Question**: Which is more economical: paying the cash price or the present value of the installment plan?

### Solution Approach for Problem 2:
This involves comparing the cash price to the present value (PV) of the installment payments, which requires discounting each monthly payment at the same interest rate.

For the present value of an annuity:
\[
PV = PMT \times \frac{1 - (1 + i)^{-n}}{i}
\]
where:
- \( PMT = 1,600 \) PHP,
- \( n = 12 \) months,
- \( i \) is the monthly interest rate.

Do you have the interest rate for these payments, or would you like help calculating with a typical rate?

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Would you like detailed calculations for either or both questions?

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### Related Questions:
1. What is the effect of compounding frequency on the total savings amount in an annuity problem?
2. How does a higher interest rate affect monthly savings needed to reach a future amount?
3. What are the advantages of choosing the cash price over installment payments when considering the time value of money?
4. How would the monthly payment change if the goal was to accumulate PHP 500,000 in 3 years instead of 5 years?
5. Can you calculate the future value of a lump-sum deposit compared to monthly savings?

### Tip:
For financial calculations, using a financial calculator or software like Excel can save time and reduce errors.

1. A student would like to save PHP 500,000 for college education in 5 years. How much should he deposit every month in a savings account if the interest is 1.4% compounded monthly?

2. A refrigerator is for sale at PHP 17,999 in cash or on terms: PHP 1,600 each month for the next 12 months. Which is lower, the cash price or the present value of the installment term?

Calculate the monthly deposit required to save PHP 500,000 for college in 5 years with 1.4% interest compounded monthly. Also, compare the cash price and present value of an installment plan for a refrigerator priced at PHP 17,999 or PHP 1,600 monthly for 12 months.

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