Question

Samantha opened a savings account and deposited $8192. The account earns 10% in interest annually. She makes no further deposits and does not withdraw any money. In t years, she has $25,710 in this account. Write an equation in terms of t that models the situation.

Answer 1

The equation in terms of t that models the situation is given by

$8192(1+\frac{0.01}{12} )^{12t} = 25710$.

We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as

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

where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.

Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710

So, we can write

$8192(1+\frac{0.01}{12} )^{12t} = 25710$

Therefore the required equation is

$8192(1+\frac{0.01}{12} )^{12t} = 25710$

Know more about compound interest here -

brainly.com/question/13870442

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