SOLUTION: 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

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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.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if you have a time value of money calculator and are allowed to use it, then you only need to know how to set the calculator up to solve the problem.

one such calculator online can be found here:

http://arachnoid.com/finance/index.html

to find out if he can invest 275 at the end of each month and whether that would be sufficient to give him 25000 at the end of 5 years, he would do the following:

set pv and fv equal to 0
set np equal to 5 * 12 = 60 monthly periods.
set pmt equal to -275 invested at the end of each month.
set ir equal to 8% / 12 = .666666667 percent for each monthly period.
select payment at end of month.
left click on fv.
calculator tells him how much he will have at the end of the 60 months, assuming all interest earned is re-invested at the same interest rate at the end of each month.
calculator tells you that fv = 20,206.14

input looks like this:

$$$

output looks like this:

$$$

that's not enough.

go back to the calculator and do the following:

pv equals 0
fv equals 25000
np = 60
pmt = 0
ir = .66666667
select payment at end of month.
left click on pmt.
calculator will tell you that you need a monthly payment of 340.24 in order to have 25000 at the end of the 5 year period.

input looks like this:

$$$

output looks like this:

$$$


the calculator works on time periods.

if you are given the interest rate percent per year and the number of years, then the interest rate percent per time period and the number of time periods are calculated as follows:

interest rate percent per time period equals interest rate per year divided by number of time periods per year.

if monthly time period, divide by 12.
if quarterly time period, divide by 4.
if weekly time period, divide by 52.
if daily time period, divide by 365 or 360 or whatever the convention is for the problem.

number of time periods equals number of years times the number of time periods per year.

if monthly time periods, multiply by 12.
if quarterly time periods, multiply by 4.
if weekly time periods, multiply by 52.
if daily time periods, multiply by 365 or 360 or whatever the convention is for the problem.

in your problem, since you had monthly time periods, the annual interest rate percent was divided by 12 and the number of years was multiplied by 12.

i verified with my own financial calculator (texas instruments business analyst 2) that these values are correct.





Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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.
The formula for the future value of an ORDINARY ANNUITY should be used, which is:, where:

 is the future value in the amount of time (years), or the amount that will be available then (UNKNOWN, in this case)

PMT is the payment amount ($275, in this case)

i is the interest rate, per year (8%, or .08, in this case)

m is the number of compounding periods per year (12, in this case)

t is the amount of time the money is invested (5, in this case)









Can you tell if he'll have enough?



The formula for the PAYMENT, per period, to an ORDINARY ANNUITY should be used. This is:, where:

 is the future value in the amount of time (years), or the amount that will be available then ($25,000, in this case)

PMT is the payment amount (UNKNOWN, in this case)

i is the interest rate, per year (8%, or .08, in this case)

m is the number of compounding periods per year (12, in this case)

t is the amount of time the money is invested (5, in this case)

Do the calculations the same way they were done above. You should get payment or  

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