Question

How much did Jonathan deposit every month in his savings account if he had $11994 after 31 month-end deposits? The money in his savings account was growing at 3.97% compounded monthly. Round to the nearest cent. Enter the result as a positive number.

Answer 1

Jonathan deposited approximately $339.63 every month into his savings account to have $11994 after 31 months with a 3.97% annual interest rate compounded monthly.

Step-by-step explanation:

To determine how much Jonathan deposited every month, we can use the formula for the future value of an annuity due to its regular deposits. The future value of an annuity formula is given by:

FV = P * (((1 + r)^n - 1) / r)

where:

• FV is the future value of the annuity (which is $11994 in Jonathan's case),
• P is the monthly deposit (what we are trying to find),
• r is the monthly interest rate (which is 3.97% annually, or 0.0397/12 per month),
• n is the number of payments (which is 31).

Rearranging the formula to solve for P, we get:

P = FV / (((1 + r)^n - 1) / r)

Substituting the values we get:

P = $11994 / (((1 + 0.0397/12)^31 - 1) / (0.0397/12))

By calculating the above, we can find out Jonathan's monthly deposit. Let's compute it:

P = $11994 / (((1 + 0.0033083)^31 - 1) / 0.0033083)

After solving through a calculator, we find that P is approximately $#8203;339.63.

Hence, Jonathan deposited about $339.63 every month in his savings account.