Question

You are preparing to make monthly payments of $65, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly. how many payments will you have made when your account balance reaches $9,278?

Answer 1

the answer is in the question

Answer 2

The total number of payments will you have made when your account balance reaches $9,278 is 52 and this can be determined by using the formula of the future value of an annuity.

Given :

• Monthly Payment of $65.
• 6 percent interest compounded monthly.
• Final amount is $9278.

The formula of the future value of an annuity can be used in order to determine the total number of payments that will be made to reach the account balance of $9278.

$FV=\dfrac{PV}{r}\left(1+r\right)^{n-1}$

where the future value is 'FV', the present value is 'PV', 'n' is the total number of times interest applied, and interest rate is 'r'.

Now, substitute the values of FV, r, and PV in the above formula.

$9278 \times 0.005=65\left(1+0.005\right)^{n-1}$

$\dfrac{49.36}{65}=\left(1.005\right)^{n-1}$

Apply log on both sides in the above expression.

$\log\dfrac{49.36}{65}=(n-1)\log \left(1.005\right)$

$n = 51.6$

So, the total number of payments will you have made when your account balance reaches $9,278 is 52.

For more information, refer to the link given below:

https://brainly.com/question/1759639