Question

Haley has deposited $816 in a savings account that earns interest at a rate of 2.9% compounded daily. what will the account balance be in nine years?

Answer 1

The answer is $1,059.34

Explanation:

The formula for compound interest is

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

Where I = interest, P = principal (original deposit), r = interest rate, n = number of times compounded per year, and t = time, in years.

Using this formula, we can substitute the information from the question for the their corresponding variables.

Now, after filling in the information, your formula should look like this

I = 816(1+$\frac{0.029}{365}$$)^{365*9}$

*The reason that the rate is 0.029 instead of 2.9 is that 2.9 is a percent, and     we need a decimal.  To convert it, you just need to divide the percent by         100.

Now, all we need to do is solve the equation using order of operations (PEMDAS).

I will divide the 0.029 by 365 first.

I = 816(1+0.00008$)^{365*9}$

**This is not the exact decimal.  It would be too difficult to write entirely, but I      will be using the true decimal in my calculations.

Next, we have to add 1 to the decimal.

I = 816(1.00008$)^{365*9}$

Now, I will multiply 365 and 9 together.

I = 816(1.00008$)^{3285}$

Next, we must raise the number within the parenthesis to the power of 3285.

I = 816(1.3)

***Again, this is not the actual decimal.  The real one will be used in the             calculation, though, like before.

Finally, we have to multiply the decimal by the principal, 816.

I = $1,059.34