Question

e. How many annual payments of $100, with the first payment right now, would it take to be worth more than $1,000, if the discount rate is 0.05? f. What is the value of 15 annual payments which begin at $100 one year from now and increase at 2% per year thereafter , if the discount rate is 0.05 ?

Answer 1

ANSWER:

E) Annual payment = $100

fv = $1,000

i = 5%

fv = 1st payment now in year 0(f/p,i,n) + payment in 2nd year(f/a,i,n)

1,000 = 100(f/p,5%,n) + 100(f/a,5%,n)

solving via trial and error we get that n is between 7 and 8 years and solving further we get that n is 7.31 years

F) In this question i don't know what we have found out that is pw or fw and so i am solving both.

Annual payment = $100

increase in payment = 2%

i = 5%

year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
cah flow		100	102	104.04	106.1208	108.24322	110.4081	112.6162	114.8686	117.1659	119.5093	121.8994	124.3374	126.8242	129.3607	131.9479

pw = cash flow in year 1(p/f,i,n) + cash flow in year 2(p/f,i,n) + cash flow in year 3(p/f,i,n) + cash flow in year 4(p/f,i,n) + cash flow in year 5(p/f,i,n) + cash flow in year 6(p/f,i,n) + cash flow in year 7(p/f,i,n) + cash flow in year 8(p/f,i,n) + cash flow in year 9(p/f,i,n) + cash flow in year 10(p/f,i,n) + cash flow in year 11(p/f,i,n) + cash flow in year 12(p/f,i,n) + cash flow in year 13(p/f,i,n) + cash flow in year 14(p/f,i,n) + cash flow in year 15(p/f,i,n)

pw = 100(p/f,5%,1) + 102(p/f,5%,2) + 104.04(p/f,5%,3) + 106.12(p/f,5%,4) + 108.24(p/f,5%,5) + 110.4(p/f,5%,6) + 112.61(p/f,5%,7) + 114.86(p/f,5%,8) + 117.16(p/f,5%,9) + 119.5(p/f,5%,10) + 121.89(p/f,5%,11) + 124.33(p/f,5%,12) + 126.82(p/f,5%,13) + 129.36(p/f,5%,14) + 131.94(p/f,5%,15)

pw = 100 * 0.9524 + 102 * 0.9070 + 104.04 * 0.8638 + 106.12 * 0.8227 + 108.24 * 0.7835 + 110.4 * 0.7462 + 112.61 * 0.7107 + 114.86 * 0.6768 + 117.16 * 0.6446 + 119.5 * 0.6139 + 121.89 * 0.5847 + 124.33 * 0.5568 + 126.82 * 0.5303 + 129.36 * 0.5051 + 131.94 * 0.481

pw = 95.24 + 92.52 + 89.87 + 87.31 + 84.81 + 82.39 + 80.03 + 77.75 + 75.53 + 73.37 + 71.27 + 69.24 + 67.26 + 65.34 + 63.47

pw = 1,175.38

fw = pw(f/p,i,n)

fw = 1,175.38(f/p,5%,15)

fw = 1,175.38 * 2.079

fw = 2,443.53

so the future worth is $2,443.53