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oksano4ka [1.4K]
3 years ago
6

$650 is invested in an account earning 8.6% interest (APR), compounded monthly. Write a function showing the value of the accoun

t after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Mathematics
1 answer:
IRISSAK [1]3 years ago
5 0

Answer:

The value of the acount after t years is of A(t) = 650(1.0072)^{12t}

The annual growth rate is of 0.72%.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

A(t) = P(1 + \frac{r}{n})^{nt}

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

$650 is invested in an account earning 8.6% interest (APR), compounded monthly.

This means that P = 650, r = 0.086, n = 12. So

A(t) = P(1 + \frac{r}{n})^{nt}

A(t) = 650(1 + \frac{0.086}{12})^{12t}

A(t) = 650(1.0072)^{12t}

The value of the acount after t years is of A(t) = 650(1.0072)^{12t}

Annual growth rate

1.0072 - 1 = 0.0072 = 0.72%

The annual growth rate is of 0.72%.

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