An Investment of $10,000 yields 8% interest compounded quarterly. The accumulated capital after 6 months is $10,404. The accumulated capital after 5 years is $14.859.47

From the information given;

The principal amount of investment = $10,000
Interest Rate = 8% = 0.08
number of times it get compounded = 4

a. we are to determine the amount of the accumulated capital after 6 months.

i.e. when time (t) = 6 months.

Now, using the formula for calculating the amount value of the accumulated capital:

$\mathbf{A = P(1 + \dfrac{r}{n})^{nt}}$

$\mathbf{A = 10000(1 + \dfrac{0.08\times 1}{4})^{4 \times \frac{1}{2}}}$

$\mathbf{A = 10000(1.02)^2}}$

A = $10,404

b. we are to determine the amount of the accumulated capital after 5 years

i.e. when time (t) = 5 years

$\mathbf{A = P(1 + \dfrac{r}{n})^{nt}}$

$\mathbf{A = 10000(1 + \dfrac{0.08\times 1}{4})^{4 \times 5}}$

$\mathbf{A = 10000(1.02)^20}}$

A = $14859.47

Therefore, we can conclude that the accumulated capital after 6 months is $10,404 and the accumulated capital after 5 years is $14859.47

Learn more about compound interest here:

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3 years ago