Ravi invests $$ \$ 4500 $$ at a rate of $$ 0.25 \% $$ per month compound interest. (a) Explain why the first year's interest is not $$ 3 \% $$ of $$ \$ 4500 $$. As he nave to pay $$ \$ 135 $$ per montn and lesser as heonly nace to pay $$ \$ 11-25 $$ (b) Calculate the value of his investment at the end of 12 months.

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**(a)**  
The rate of $$0.25\%$$ per month is applied to the balance each month. In compound interest, the interest earned in each month is added to the principal, and the next month's interest is computed on this increased amount. Therefore, rather than simply being a fixed $$3\%$$ of the initial $$ \$4500 $$ (which would be the case if interest were calculated only on the original amount), the interest is earned on a gradually increasing balance over the year. In effect, the effective annual rate is given by  
$$
(1+0.0025)^{12}-1
$$  
which is slightly greater than $$3\%$$.

**(b)**  
To calculate the value of the investment after 12 months, we use the compound interest formula:  
$$
A = P(1+r)^n,
$$  
where

- $$P = 4500$$ (initial investment),
- $$r = 0.0025$$ (monthly interest rate),
- $$n = 12$$ (number of months).

Substitute the values into the formula:
$$
A = 4500(1.0025)^{12}.
$$

Computing $$(1.0025)^{12}$$:
$$
(1.0025)^{12} \approx 1.03042.
$$

Thus, the value of the investment at the end of 12 months is:
$$
A \approx 4500 \times 1.03042 \approx 4636.89.
$$

Ravi’s investment will be approximately $$\$4636.89$$ at the end of 12 months.
**(a)** The interest isn't $$3\%$$ because it's compounded monthly. Each month, the interest is calculated on the new balance, which grows slightly each time. So, the total interest over the year is a bit more than $$3\%$$. **(b)** After 12 months, Ravi's investment will be approximately \$4,636.89.

Ravi invests at a rate of per month compound interest.
(a) Explain why the first year’s interest is not of .
As he nave to pay per montn and
lesser as heonly nace to pay
(b) Calculate the value of his investment at the end of 12 months.

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Ravi invests at a rate of per month compound interest. (a) Explain why the first year’s interest is not of . As he nave to pay per montn and lesser as heonly nace to pay (b) Calculate the value of his investment at the end of 12 months.