Question 622653: Suppose Mary deposits $200 at the end of each month for 30 years into an account tht pays 5% interest compounded monthly.
a. How much total money will she have in the account at the end?
b. How much total money did Mary actually deposit?
c. How much total interest did the account earn over that period?
d. Suppose instead of making monthly deposits, Maryb decides to deposit a "lump sum" into the account. How much must she deposit? What is the value also called?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! monthly payments are $200 for 30 * 12 = 360 months.
payments are made at the end of each month.
monthly interest rate is 5% per year divided by 12 equals (5/12)% per month.
That equates to an interest rate of .004166666... per month.
Using the TI-BA-II financial calculator, I do the following:
Set the monthly payments to end of month if they are not already set there.
Set PMT to 200
Set I/Y to (5/12)
Set N to 30*12
Set PV to 0
Set BGN (2ND-FV) to END.
Compute FV
a. How much total money will she have in the account at the end?
Mary has $166,451.7271 in the account at the end of 360 months.
b. How much total money did Mary actually deposit?
Mary deposited a total oof 360 * 200 = $72,000
c. How much total interest did the account earn over that period?
The account earned $166,451.73 - $72,000 = $94,451.73 in interest over that period.
d. Suppose instead of making monthly deposits, Mary decides to deposit a "lump sum" into the account. How much must she deposit? What is the value also called?
We are talking about a future value of $166,451.7271 for a period of 360 months at a monthly interest rate of (5/12)% per month.
The interest rate per month and the number of months is the same as we used in the calculation of the Future Value from a Payment.
This time we use the Present Value of a Future Amount Formula.
In the TI-BA-II, the inputs are as follows:
N = 360
I/Y = (5/12)
PV = 0
PMT = 0
FV = 166451.7271
Compute PF by entering CPT then PV
The answer is that she would have to invest $37,256.32341 up front so that she can have the same amount in the future as she did with the monthly payments.
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Use of a financial calculator such as the TI-BA-II makes it easy.
The formula to use manually can be found in the following link:
http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson
The formula you would use would be FUTURE VALUE OF A PAYMENT
The interest rate used is the percent divided by 100%.
Where I used 5/12 as the percent interest in the calculator, you would use 5/1200.
Everything else is pretty much the same, i.e. plugging the values in the formula and then determining the result.
The number of time periods is the same as the number of months.
You take the number of years and multiply them by 12 to get the number of time periods.
The monthly interest rate is the annual interest rate divided by 12 which is 5 / 1200.
The total payments made are the number of time periods times the payment per time period.
The total interest is the total money earned (Future Value) minus the total payments made.
For part d, the manual formula to be used is the PRESENT VALUE OF A FUTURE AMOUNT
Future Amount is equal to 166,451.7271
Present Value is what you're looking to find.
i is the interest rate per time period which is 5/1200 (use rate for manual calculation and not percent).
n is the number of time periods which is 30 * 12 = 360.
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