Question

1. what is the pv of an ordinary annuity with 10 payments of 4100 if the appropriate interest rate is 5%?
2. Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $53000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7%. How much would it cost her to buy such an annuity today?
3. What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,800 at the end of Year 4 if the interest rate is 5%?
4. What annual payment must you receive in order to earn a 6% rate of return on a 4 year annuity that has a cost of $2600?
5. What's the present value of $11500 discounted back 5 years if the appropriate interest rate is 4%, compounded semianually?
6. Suppose you borrowed $30,000 at a rate of 8% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year.

Answer 1

1)

	Present value of annuity	P×[1-(1÷(1+r)^n)]÷r
	Here,
A	Interest rate per annum	5.00%
B	Number of years	10
C	Number of compoundings per per annum	1
A÷C	Interest rate per period ( r)	5.00%
B×C	Number of periods (n)	10
	Payment per period (P)	$                                          4,100
	Present value of annuity	$       31,659.11
		4100×(1-(1÷(1+5%)^10))÷5%