Question

You have just purchased a pre-owned house. The inspector notified you that since the root on the house is 12 years old, it would need to be replaced 8 years from now. In order to plan for the major expense of replacing the roof, you decided to set up a savings account in which you plan to make annual deposits as shown in Table 1. If the account can earn an effective annual interest rate of 2% a. Draw a fully labeled cash flow diagram of your deposits into the account from your point of you (10 points) b. Setup the equations to calculate the savings account balance at the EOY 8 (14 points) c. Calculate the savings account balance at EOY 8 (1 points) Table 1 EOY Deposit $500 $500 $500 $500 $500 $500 $1,000 $1,000 8 $1,000

Answer 1

We have the following information

EOY	Deposit ($)
0	500
1	500
2	500
3	500
4	500
5	500
6	1000
7	1000
8	1000

n = Number of interest periods = 8 years

i = Interest rate = 2% or 0.02

Future Balance in Saving Account = 500 + 500(F/A, 2%, 5) + 1000(1 + 0.02)⁶ + 1000(1 + 0.02)⁷ + 1000(1 + 0.02)⁸

Future Balance in Saving Account = 500 + 500[((1 + 0.02)⁵ – 1)/0.02] + 1126.16 + 1148.69 + 1171.66

Future Balance in Saving Account = 500 + (500 × 5.204) + 3446.51

Future Balance in Saving Account = 500 + 2602.02 + 3446.51

Future Balance in Saving Account = $6,548.53

$6548-53 $500 $500 $500 $500 $500 $500 $1000 $1000 $1060 Scanned with Camscanner