Question

What is the present value of a five-period annuity of $3,000 if the interest rate per period is 12% and the first payment is made today?

Three thousand dollars is deposited into an account paying 10% annually to provide three annual withdrawals of $1,206.34 beginning in one year. How much remains in the account after the second payment has been withdrawn?

You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%?

Answer 1

i). Five year period Annuity = $3,000

Interest rate = 12%

Calculating the Present value of Annuity as the first payment is made today:-

Where, C= Periodic Payments =$3,000

r = Periodic Interest rate = 0.12

n= no of periods =5

So, The Present Value is $ 12,112.05

ii). $3000 is deposited in an account that along with periodic interest accumulate such amount that it can be withdrawal equally using 3 annual withdrawal amount of $ 1206.34

Since, the withdrawal will start at the year end. The account will earn Interest each year on the amount left after withdrawal. So, the last withdrawal of $ 1206.34 will also has interest included in itself of the last year.

Computiting the Balance amount after second payment or last withdrawal amount before Interest:-

Account Balance = Withdrawal Amount/(1+Interest)

=$1206.34/(1+0.10)

=$1096.67

iii). Calculating the Present Value of the Cash flows:-

Year	Cash Flows ($)	PV Factor @7.00%	Present Value ($)
0	1,000.00	1.0000	1,000.00
1	2,000.00	0.9346	1,869.16
3	4,000.00	0.8163	3,265.19
5	6,000.00	0.7130	4,277.92
			10,412.27

So, the present value of these cash flows at an interest rate of 7% is $10,412.27

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