The following five situations require the use of future and present values. Calc

Question

The following five situations require the use of future and present values. Calculate the amounts requested, rounding all answers to the nearest dollar. If you deposited $20,000 in a savings account at 5 percent interest, compounded quarterly how much would be in the savings account at the end of 8 years? How much cash would you have to deposit today in a savings account to have $125,000 at the end of 10 years, assuming an annual interest rate of 12 percent, compounded monthly? If you deposited $800 per quarter, at the end of each quarter, in a retirement account earning 8 percent interest per year, how much would be in the savings account at the end of 20 years? How much cash would you have to deposit at the end of each year to have $2S0.000 at d of 10 years assuming an interest rate of 9 percent per year? You have just purchased a new auto that cost $30,000. You paid $3,000 down and financed the balance over 72 months at 4% interest per year (beginning of the month paymentprincipal and interest). How much will your monthly payment be?

Explanation / Answer

Since, there are multiple parts, the first four have been answered.

__________

Part 1)

The future value can be calculated with the use of following formula:

Future Value = Amount*(1+Interest Rate/4)^(Years*4) [we use 4 because the compounding is quarterly]

___________

Using the information provided in the question, we get,

Future Value after 8 Years = 20,000*(1+5%/4)^(8*4) = $29,762.61 (answer)

___________

Part 2)

We will have to use the following present value formula to calculate the amount to be deposited today to received $125,000 at the end of 10 Years.

Present Value = Amount Desired/(1+Interest Rate/12)^(Years*12) [we use 12 since the compounding is monthly]

___________

Using the information provided in the question, we get,

Amount to be Deposited Today = 125,000/(1+12%/12)^(10*12) = $37,874.35 (answer)

___________

Part 3)

To determine the amount after 20 years, we need to calculate the future value of annuity of $800 per quarter. The future value of an annuity can be calculated with the use of FV function/formula of EXCEL/Financial Calculator. The function/formula for FV is FV(Rate,Nper,PMT,PV) where Rate = Interest Rate, Nper = Period, PMT = Amount of Deposit and PV = Present Value (if any).

___________

Here, Rate = 8%/4, Nper = 4*20 = 80, PMT = $800 and PV = 0 [we use 4 since the deposits are made quarterly]

Using these values in the above function/formula for FV, we get,

Amount after 20 Years = FV(8%/4,80,800,0) = $155,017.57 (answer)

___________

Part 4)

The amount to be deposited each year can be calculated with the use of Payment (PMT) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value (if any) and FV = Future Value.

___________

Here, Rate = 9%, Nper = 10, PV = 0 and FV = $250,000

Using these values in the above function/formula for PMT, we get,

Amount to be Deposited Each Year = PMT(9%,10,0,250000) = $16,455.02 (answer)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.