Question

A certain homeowner's insurance bill is $1,200 this year. Insurance rates are expected to increase at a rate of 7% per year for the next 10 years. If interest is 10% the equivalent uniform annual insurance bill over the 11-year period (i.e.,on payment now and 10 future payments) is closest to....

a) $9,633

b) $1,572

c) $1,488

d) $6,000

e) $5,121

f) $4,736

g) $1,494

h) $9,112

I) $1,818

j) $2,033

k) $1,616

Answer 1

ANSWER:

Insurance bill in year 1 = $1,200

Insurance bill in year 2 = Insurance bill in year 1 +  Insurance bill in year 1 * increase in rate = 1200 + 1200 * 7% = 1200 + 84 = 1284

Insurance bill in year 3 = Insurance bill in year 2 +  Insurance bill in year 2 * increase in rate = 1284 + 1284 * 7% = 1284 + 89.88 = 1373.88

Insurance bill in year 4 = Insurance bill in year 3 +  Insurance bill in year 3 * increase in rate = 1373.88 + 1373.88 * 7% = 1373.88 + 96.17 = 1470.05

Insurance bill in year 5 = Insurance bill in year 4 +  Insurance bill in year 4 * increase in rate = 1470.05 + 1470.05 * 7% = 1470.05 + 102.90 = 1572.95

Insurance bill in year 6 = Insurance bill in year 5 +  Insurance bill in year 5 * increase in rate = 1572.95 + 1572.95 * 7% = 1572.95 + 110.1 = 1683.06

Insurance bill in year 7 = Insurance bill in year 6 +  Insurance bill in year 6 * increase in rate = 1683.06 + 1683.06 * 7% = 1683.06 + 117.81 = 1800.87

Insurance bill in year 8 = Insurance bill in year 7 +  Insurance bill in year 7 * increase in rate = 1800.87 + 1800.87 * 7% = 1800.87 + 126.06 = 1926.03

Insurance bill in year 9 = Insurance bill in year 8 +  Insurance bill in year 8 * increase in rate = 1926.03 + 1926.03 * 7% = 1926.03 + 134.88 = 2061.82

Insurance bill in year 10 = Insurance bill in year 9 +  Insurance bill in year 9 * increase in rate = 2061.82 + 2061.82 * 7% = 2061.82 + 144.32 = 2206.15

Insurance bill in year 11 = Insurance bill in year 10 +  Insurance bill in year 10 * increase in rate = 2206.15 + 2206.15 * 7% = 2206.15 + 154.43 = 2360.58

now we will find the present worth of these cash flows.

i =10% and n = 11 years

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)

pw = 1200(p/f,10%,1) + 1284(p/f,10%,2) + 1373.88(p/f,10%,3) + 1470.05(p/f,10%,4) + 1572.95(p/f,10%,5) + 1683.06(p/f,10%,6) + 1800.87(p/f,10%,7) + 1926.93(p/f,10%,8) + 2061.82(p/f,10%,9) + 2206.15(p/f,10%,10) + 2360.58(p/f,10%,11)

pw = 1200 * 0.9091 + 1284 * 0.8264 + 1373.88 * 0.7513 + 1470.05 * 0.683 + 1572.95 * 0.6209 + 1683.06 * 0.5645 + 1800.87 * 0.5132 + 1926.93 * 0.4665 + 2061.82 * 0.4241 + 2206.15 * 0.3855 + 2360.58 * 0.3505

pw = 1,090.91 + 1,061.16 + 1,032.22 + 1,004.07 + 976.68 + 950.04 + 924.13 + 898.93 + 874.41 + 850.57 + 827.37

pw = 10,490.49

now we will the uniform annual insurance cost.

aw = pw(a/p,i,n)

aw = 10,490.49(a/p,10%,11)

aw = 10,490.49 * 0.154

aw = 1,615.53

so the unifor annual cost of insurance is $1,616 (rounded off) that is option k.