Question

Calculating the number of payments you're prepared to make monthly payments of 190, beginning at the end of this month, into an account that pays 7 percent interest compounded monthly. How many payments will you have made when your account balance reaches 20,000?

Answer 1

The number of monthly payments until the account balance reaches $20,000 with monthly payments of $190 at 7% interest compounded monthly can be determined using the future value of an annuity formula. By rearranging the formula to solve for the number of payments and substituting the given values, one can find the number of payments required.

Step-by-step explanation:

To calculate the number of monthly payments you will make until the account balance reaches $20,000 with monthly payments of $190 at a 7 percent interest rate compounded monthly, we can use the future value of an annuity formula:

FV = P × { [(1 + r)^n - 1] / r }

Where:

• FV is the future value of the annuity, which is $20,000 in this case.
• P is the monthly payment amount, which is $190.
• r is the monthly interest rate, which is 7% annually or 0.07/12 per month.
• n is the number of payments, which is what we're solving for.

Rearranging the formula to solve for n, we get:

n = log((FV×r/P) + 1) / log(1+r)

Substituting the given values into this formula:

n = log(($20,000×(0.07/12)/$190) + 1) / log(1+(0.07/12))

When you calculate it, you’ll find the number of payments that will be made until the account balance reaches $20,000. Note that this is a general approach and for exact figures, you may need to use a financial calculator or software designed for such computations.