Question 1030447
Seems the interest, and money story problems give me the hardest time.. 

Mitch is tired of renting and decides that within the next 5 years he must save $25,000.00 for the down payment on a home. He finds an investment company that offers 8% interest compounded monthly and begins depositing $275 each month in the account.

A.) Is this monthly amount sufficient to help him meet his 5-year goal?

B.) If not, find the minimum amount he needs to deposit each month that will enable him to meet his goal in 5 years?

Please show all work, in hopes that I can understand afterwards.
<pre>The formula for the future value of an ORDINARY ANNUITY should be used, which is:{{{FV[oa] = PMT * ((1 + i/m)^(mt) -1) * (m/i)))}}}, where:
{{{FV[oa]}}} is the future value in the amount of time (years), or the amount that will be available then <font color="red"><b>(UNKNOWN, in this case)</font></b>
PMT is the payment amount <font color="red"><b>($275, in this case)</font></b>
i is the interest rate, per year <font color="red"><b>(8%, or .08, in this case)</font></b>
m is the number of compounding periods per year <font color="red"><b>(12, in this case)</font></b>
t is the amount of time the money is invested <font color="red"><b>(5, in this case)</font></b>
{{{FV[oa] = PMT * ((1 + i/m)^(mt) -1) * (m/i)))}}}
{{{FV[oa] = 275 * ((1 + .08/12)^(12 * 5) - 1) * (12/.08)))}}}
{{{FV[oa] = 275 * ((1 + .08/12)^60 - 1) * 150))}}}
{{{highlight(highlight_green(highlight(matrix(1,3, FV[oa], "=", "$20,206.14"))))}}}
Can you tell if he'll have enough?

The formula for the PAYMENT, per period, to an ORDINARY ANNUITY should be used. This is:{{{PMT = FV[oa]/((1 + i/m)^(mt) - 1 * (m/i))}}}, where:
{{{FV[oa]}}} is the future value in the amount of time (years), or the amount that will be available then <font color="red"><b>($25,000, in this case)</font></b>
PMT is the payment amount <font color="red"><b>(UNKNOWN, in this case)</font></b>
i is the interest rate, per year <font color="red"><b>(8%, or .08, in this case)</font></b>
m is the number of compounding periods per year <font color="red"><b>(12, in this case)</font></b>
t is the amount of time the money is invested <font color="red"><b>(5, in this case)</font></b>
Do the calculations the same way they were done above. You should get payment or {{{highlight(highlight_green(highlight(matrix(1,3, PMT, "=", "$340.24"))))}}}