Please provide an explanation of all answers included which formulas you used. 1

Question

Please provide an explanation of all answers included which formulas you used.

1Your grandmother invested one lump sum 17 years ago at 4.25 percent interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest? Round to the nearest cent. Do not include any unit (i.e. $, %, etc.)

2 Your grandparents are talking about their retirement in a year. They told you that they should have enough in their retirement funds to pull $50,000 a year for 20 years, starting one year from today. If the discount rate is 5 percent, how much should they have in their retirement account now? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

3You purchased Honda Civic for $18,290 today. You took an auto loan at the annual interest rate of 3.65%. You are going to make equal monthly payment for next 6 years starting a month from now. How much is your monthly car payment? Round to the nearest cent. Do not include any unit (If your answer is $111.11, then type 111.11 without $ sign.)

Explanation / Answer

1)

We need to find the present value of 5,539.92.

Present value = Future value / ( 1 + r)n

Present value = 5,539.92 / ( 1 + 0.0425)17

Present value = 5,539.92 / 2.029052

Present value = 2,730.3

2)

We need to find the present value of annuity of 50,000. Annuity is a fixed series of cash flows for a fixed period of time.

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + r)n] / r

Present value of annuity = 50,000 * [ 1 - 1 / ( 1 + 0.05)20] / 0.05

Present value of annuity = 50,000 * 12.46221

Present value of annuity = 623,110.5

3)

Number of periods = 6 * 12 = 72 ( since it is monthly compounding , we multiply by 12)

Rate = 0.0365 / 12 = 0.003042 or 0.3042% ( since it is monthly compounding , we divide by12)

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + r)n] / r

18,290 = Annuity * [ 1 - 1 / ( 1 + 0.003042)72] / 0.003042

18,290 = Annuity * 64.572797

Annuity = 283.2

Monthly car payment will be 283.2

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

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