Question

a. Your investment account is expected to earn a 5% return for next two years and then 8% return for next four years after that. You need to withdraw $750 from this account at the end of each month for next six years. After last withdrawal at end of six years, nothing remains in your account. how much is deposited in this account today? (Assume monthly compounding)

b. You just bought a condo for $250,000 and paid $50,000 as down payment. The remaining amount is financed through a loan of 4.5% compounded monthly. The loan is for 15 years. You have to make monthly payments at the end of each month. What is your monthly payment? What is the balance of this loan after ten years? What is the total interest paid on this loan for 15 years?

Answer 1

a)

here first we have to calculate present value for first 2 years and then for 4 years then we have to add both to arrive at persent value

Using financial calculator:

calculating PV for the first 2 years (i.e., 24 months) (present value at t = 0)

[N = 24 ; I/Y = 5%/12 ; PV = ? ; PMT = 750 ; FV = 0 ] compute( CPT button) for PV

present value = 17,095.42 (this is at t = 0)

calculating present value for the next 4 years (48 periods) (Present value at t = 2)

here interest rate = 8%/12

[N = 48 ; I/Y = 8%/12 ; PV = ? PMT = 750 ; FV = 0]

Present value = $30,721.43 (this is at t = 2)

Now we have to bring above present value to time period t = 0, here interest rate will be 5%/12

[N = 24 ; I/Y = 5%/12 ; PV = ? PMT = 0 ; FV = 30,721.43]

Present value at t = 0 will be = 27,803.68

Total Present value = 17,095.42 + 27,803.68 = $44,899.10

So we must Deposit $44,899.10 today

b)

Condo value = 250,000

Down payment = 50,000

so loan amount = 250,000 - 50,000 = 200,000

Time period = 15*12 = 180

Interest rate = 4.5%/12

[N = 180 ; I/Y = 4.5%/12 ; PV = 200000 ; PMT = ? ; FV = 0] compute for PMT

so monthly payments = $1530

Balance after 10 years:

remaining period after 10 years = 5 years (i.e., 5*12 = 60 periods)

we have to calculate PV using calculator

[N = 60 ; I/Y = 4.5%/12 ; PV = ? PMT = 1530 ; FV = 0] compute PV

Loan balance after 10 years = $82,067.53

Total interest paid:

Total amount paid - loan amount

Total amount Paid = 180*1530 = $275,397.58

Interest = 275,397.58 - 200,000 = $75397.58