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 2 years ago

Find the PV of an annuity payable in arrears of $1,000 p.a. payable quarterly for 25...

Find the PV of an annuity payable in arrears of $1,000 p.a. payable quarterly for 25 years at an effective rate of interest of 6% p.a

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%.

If the PV of an ordinary four year annuity is $1000 with an interest rate of...

If the PV of an ordinary four year annuity is $1000 with an interest rate of 6%, what is the FV if were an annuity due instead?

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.

Question