Question

When dante was born, his grandparents deposited $10,000 into a special college fund that paid 4% annual interest, compounded monthly. how old was dante when the balance in the account reached$13,000? round your answer to the nearest tenth of a year.

Answer 1

Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

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

In which:

• 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.

In this problem, we have that the parameters are given as follows:

A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.

Hence the time in years is found as follows:

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

$13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}$

$(1.0033)^{12t} = 1.3$

$\log{(1.0033)^{12t}} = \log{1.3}$

$12t\log{1.0033} = \log{1.3}$

$t = \frac{\log{1.3}}{12\log{1.0033}}$

t = 6.6

More can be learned about compound interest at brainly.com/question/25781328

#SPJ1