To calculate the future value of the time deposit account, we use the formula for compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the future value of the investment.
• $P$ is the principal amount (initial investment).
• $r$ is the annual nominal interest rate (as a decimal).
• $n$ is the number of compounding periods per year.
• $t$ is the time in years.

Given:

• $P = 100,000$
• $r = 4.5\% = 0.045$
• $n = 4$ (quarterly compounding)
• $t = 5$

Plugging in the values:

$A = 100,000 \left(1 + \frac{0.045}{4}\right)^{4 \cdot 5}$

Simplify step-by-step:

1. Calculate $\frac{0.045}{4}$: $\frac{0.045}{4} = 0.01125$

2. Add 1 to get the base of the exponent: $1 + 0.01125 = 1.01125$

3. Calculate the exponent $4 \cdot 5 = 20$.

4. Raise $1.01125$ to the power of 20: $1.01125^{20} \approx 1.243006$

5. Multiply by $100,000$: $A = 100,000 \cdot 1.243006 = 124,300.60$

Final Answer:

At the end of five years, the amount in the account will be ₱124,300.60.

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Would you like further details or have any questions?

Related Questions:

1. What is the formula for simple interest and how does it differ from compound interest?
2. How does the frequency of compounding affect the future value of an investment?
3. Can the same formula be used for non-annual compounding intervals like monthly or daily?
4. What would happen to the final amount if the interest rate were 6% instead of 4.5%?
5. How can we calculate the interest earned instead of the total amount?

Tip:

When compounding, the more frequent the intervals, the higher the accumulated value, as interest earns interest more frequently.