Question

6a. What is the present value of $1,000,000, due 25 years from now? b. What is the present value of a $40,000 ordinary annuity for 25 years? c. What is the present value of a $40,000 perpetuity, if the first payment is 1 year from now? d. What is the present value of a $40,000 perpetuity, if the first payment is now? 7. You borrow $35,000 today and will make equal annual payments for the next 3 years, starting in 1 year. a. What is the value of the annual payment if the nominal interest on the loan is: 9.50% Payment b. Show the amortization of the loan in the table set up below: Year Beg. Balance Payment Interest Principal Ending Balance 1 2 3 TOTAL

Nominal interest rate =10%

Answer 1

Q6a) We are given the following information:

Value of account at time 0	PV	To be calculated
rate of interest	r	10.00%
number of years	n	25
Future value	FV	$ 10,00,000.00

We need to solve the following equation to arrive at the required FV

6b)

Annual payment	PMT	$        40,000.00
rate of interest	r	10.00%
number of years	n	25
Present value	PV	To be calculated

6c)PV of perpetuity when the first payment is due one year from now is calculated as follows:

6d)PV of perpetuity when the first payment is due now is calculated as follows:

Q7)We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	9.50%
Number of years	n	3.00
Annual	frequency	1.00
Loan amount	PV	35000.00

We need to solve the following equation to arrive at the required PMT

So the annual payment is $13950.30

Year	Beg Balance	PMT	Interest	Principal repayment	Ending Balance
1	$            35,000.00	$       13,950.30	$         3,325.00	$                   10,625.30	$         24,374.70
2	$            24,374.70	$       13,950.30	$         2,315.60	$                   11,634.70	$         12,740.00
3	$            12,740.00	$       13,950.30	$         1,210.30	$                   12,740.00	$                  -0.00
		$       41,850.90	$         6,850.90	$                   35,000.00

Opening balance = previous year's closing balance
Closing balance = Opening balance-Principal repayment
PMT is calculated as per the above formula
Interest = 0.095 /12 x opening balance
Principal repayment = PMT - Interest