Question

What is the present value of $100 per month at a discount rate of 6%, if the first payment is received 5 years from now and the last payment is received 18 years from now?

Given a 6 percent discount rate compounded quarterly, what is the present value of a perpetuity of $100 per month if the first payment does not begin until the end of year five?

You are planning to save for retirement over the next 25 years. To do this, you will invest $3,000 a quarter in a stock account and $1,000 a quarter in a bond account. These investments will be made at the beginning of each quarter. The return of the stock account is expected to be 8%, and the bond account will pay 4%. When you retire, you will combine your money into an account with a 6% return. How much can you withdraw each month (starting one month from the retirement date) from your account assuming a 20-year withdrawal period?

Answer 1

Solution:

Solving question first as per chegg's guideline:

1.Calculation of Present value:

First,we need to calculate the present value $100 per month at the end of 5th year

No. of payments=$100*12*(18-5)

=15,600

Discount rate(r)=6% p.a

no. of compounding(m)=12

Present value of $100 annuity=$100*Present value annuity factor

=($100/0.06/12)*[1-1/(1+0.06/12)](1+0.06/12)

=$10912.28

Now,calculate the present value of $10912.28 today using the following formula:

=Future value*1/(1+r)^no. of years

=$10,912.28*1/(1+0.06)^5

=$10,912.28*0.7472582

=$8,154.29