Question text Find the PV of an annuity, which starts at $1 per year (payable at...

Question text

Find the PV of an annuity, which starts at $1 per year (payable at the end of the year) and increases by $1 per year to a value of $15, then decreases by $1 per year to the final payment of $1. Assume i = 0.07

Expert Solution

PV is calculated as follows

Year	CF	Discount Factor	Discounted CF
1	$ 1.00	1/(1+0.07)^1=	0.934579439	0.934579439252336*1=	0.93
2	$ 2.00	1/(1+0.07)^2=	0.873438728	0.873438728273212*2=	1.75
3	$ 3.00	1/(1+0.07)^3=	0.816297877	0.816297876890852*3=	2.45
4	$ 4.00	1/(1+0.07)^4=	0.762895212	0.762895212047525*4=	3.05
5	$ 5.00	1/(1+0.07)^5=	0.712986179	0.712986179483668*5=	3.56
5	$ 6.00	1/(1+0.07)^5=	0.712986179	0.712986179483668*6=	4.28
7	$ 7.00	1/(1+0.07)^7=	0.622749742	0.622749741884591*7=	4.36
8	$ 8.00	1/(1+0.07)^8=	0.582009105	0.582009104565038*8=	4.66
9	$ 9.00	1/(1+0.07)^9=	0.543933743	0.543933742584148*9=	4.90
10	$ 10.00	1/(1+0.07)^10=	0.508349292	0.508349292134718*10=	5.08
11	$ 11.00	1/(1+0.07)^11=	0.475092796	0.475092796387587*11=	5.23
12	$ 12.00	1/(1+0.07)^12=	0.444011959	0.444011959240735*12=	5.33
13	$ 13.00	1/(1+0.07)^13=	0.414964448	0.414964447888538*13=	5.39
14	$ 14.00	1/(1+0.07)^14=	0.387817241	0.387817241017325*14=	5.43
15	$ 15.00	1/(1+0.07)^15=	0.36244602	0.36244601964236*15=	5.44
16	$ 14.00	1/(1+0.07)^16=	0.338734598	0.338734597796598*14=	4.74
17	$ 13.00	1/(1+0.07)^17=	0.31657439	0.31657439046411*13=	4.12
18	$ 12.00	1/(1+0.07)^18=	0.295863916	0.295863916321598*12=	3.55
19	$ 11.00	1/(1+0.07)^19=	0.276508333	0.276508333010839*11=	3.04
20	$ 10.00	1/(1+0.07)^20=	0.258419003	0.258419002813869*10=	2.58
21	$ 9.00	1/(1+0.07)^21=	0.241513087	0.241513086741933*9=	2.17
22	$ 8.00	1/(1+0.07)^22=	0.225713165	0.225713165179377*8=	1.81
23	$ 7.00	1/(1+0.07)^23=	0.210946883	0.210946883345212*7=	1.48
24	$ 6.00	1/(1+0.07)^24=	0.19714662	0.197146619948796*6=	1.18
25	$ 5.00	1/(1+0.07)^25=	0.184249178	0.18424917752224*5=	0.92
26	$ 4.00	1/(1+0.07)^26=	0.172195493	0.172195493011439*4=	0.69
27	$ 3.00	1/(1+0.07)^27=	0.160930367	0.16093036730041*3=	0.48
28	$ 2.00	1/(1+0.07)^28=	0.150402212	0.15040221243029*2=	0.30
29	$ 1.00	1/(1+0.07)^29=	0.140562815	0.140562815355411*1=	0.14
				PV = Sum of all Discounted CF	89.04

PV comes to 89.04

jeff jeffy answered 1 year ago

1. Present Value of $1 Annuity Table: Find the PV of $1/year annuity for each period...

1. Present Value of $1 Annuity Table: Find the PV of $1/year annuity for each period and discount rate in the table below. Period 8% 10% 20% 10 15 30

A loan is to be repaid by annuity payable annually in arrears. The annuity starts at...

A loan is to be repaid by annuity payable annually in arrears. The annuity starts at rate of Kshs. 300 per annum and increases each year by Kshs. 30 per annum. The annuity is repaid for 20 years and repayments are calculated using a rate of interest of 7% per annum effective. Calculate i) The original amount of the loan [1Mk] ii) The capital outstanding immediately after 5th payment has been made [2Mks] iii) The capital and interest components of...

Find the PV of a 15-year annuity-immediate with payments of 15, 14, 13, ..., 1 at...

Find the PV of a 15-year annuity-immediate with payments of 15, 14, 13, ..., 1 at an annual effective rate of interest i = 3%. Find the PV of a 26-year annuity-immediate with payments of 1, 2, 3, ..., 26 at an annual effective rate of interest i= 7%.

Find the PV of a 26-year annuity-immediate with payments of 1, 2, 3, ..., 26 at...

Find the PV of a 26-year annuity-immediate with payments of 1, 2, 3, ..., 26 at an annual effective rate of interest i = 7%.

1. Find the present value of a ten-year annuity which pays $600 at the beginning of...

1. Find the present value of a ten-year annuity which pays $600 at the beginning of each quarter for the first 5 years, and then $500 at the beginning of each quarter for the remaining years. The annual effective interest rate is 5%. Round your answer to two decimal places. 2. A bank makes payments continuously at a rate of $260 per year. The payments are made between times 6 and 9 (measured in years). Find the present value of...

Future Value of $1 Annuity Table: Find the FV of $1/year annuity for each period and...

Future Value of $1 Annuity Table: Find the FV of $1/year annuity for each period and discount rate in the table below. Period 8% 10% 20% 10 15 30

Find the Future Value of an ordinary annuity that pays $600 per year for 5 years...

Find the Future Value of an ordinary annuity that pays $600 per year for 5 years at 4%. Compounding occurs once a year. $2,187.31 $3,249.79 $729.99 $2,671.10 $2,586.08

Find the net single premium for a 10-year life annuity due of 25.000€ per year (starting...

Find the net single premium for a 10-year life annuity due of 25.000€ per year (starting at the signature of the contract) issued to a female at her 60th birthday, using an interest rate of 3.5%/year. Mortality rate can be random. The point is the calculation, excluding any other (rates, numbers etc.) Just working with what is given.

PV of a Growing Annuity An investment offers the following cash flows: $1000 in one year,...

PV of a Growing Annuity An investment offers the following cash flows: $1000 in one year, followed by 9 more annual payments (years 2-10) that grow at a rate of 7% per year. If your opportunity cost is 8% per year, the PV today of this stream of cash flows is $______________. Margin of error for correct responses: +/- $.05.

1.there is an example of a three-year annuity, which the first payment is in year 1,...

1.there is an example of a three-year annuity, which the first payment is in year 1, the second payment in year 2, and the third payment is in year 3. However, if the first payment will be paid in the second year, how can I calculate the present value of such annuity. 2.Why the annuity due's result in a higher present value? If you have cash outflow, wouldn't your money be less and the present value shouldn't be decreased? 3.It...

Question