SOLUTION: This is Business Math. Please use the financial calculator BAII Plus for this. A deposit of $4,200 is made today for a period of five years. For how long can $500 be withdrawn f

Question 1201630: This is Business Math. Please use the financial calculator BAII Plus for this.
A deposit of $4,200 is made today for a period of five years. For how long can $500 be withdrawn from the account at the end of every three months starting three months after the end of the five year term if the interest is 5.75% compounded quarterly?
a. What is the annuity worth after the deferral period?
b. What is the value of N? (Correct to 8 decimal places)
c. How many payments? (Round n up to the next payment)
d. The term of the annuity will be ____ years and ______ months. (These answers are both whole numbers, no decimals)
Hint: as the question deals with quarters months can only be in blocks of 3)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
4200 deposited today.
interest rate is 5.75% compounded quarterly = 1.4375% per quarter.
5 years * 4 quarters per year = 20 quarters.
the future value at the end of the 5 year investment period is equal to 5587.532134.
that becomes the present value of the annuity that starts at the end of the 5 year investment period.
you will be withdrawing 500 at the end of each quarter after that.
the annuity will be depleted after 12.26943235 quarters.
the number of payments will be equal to 13 quarterly payments.
the last quasrterly payment will be for the remaining balance, which will be less than 500.
excel says the last payment at the end of the 13th quarter will be equal to 135.42 rounded to the nearest penny.
the term of the 13 payments is equal to 3 years and 3 months.
this is what it will look like in excel.

an online calculator similar to the ti-ba-ii can be found at https://arachnoid.com/finance/

the results from using that calculator are shown below.

that calculator differs in that it rounds the results to less decimal places than the ti-ba-ii.

a you can see, the results are very close to what the ti-ba-ii calculated, once you take into account the rounding.

the first calculation was to find the future value.
the second calcultion was to find the numbers of quarters the loan required.
the future value became the present value of the annuity.

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