Question

This question about " Engineering Economics ".

Notes:

Please draw cashflow diagram before start the solution.

Use standard notation equations.

The question is:

Ahmed deposits $1,000 in a savings account; 4 years after the deposit, half of the account balance is withdrawn. $2,000 is deposited annually for an 8-year period, with the first deposit occurring 2 years after the withdrawal. The total balance is withdrawn 15 years after the initial deposit. If the account earned interest of 8% compounded annually over the 15-year period, how much was withdrawn at each withdrawal point?

O $22,859.27

O $27,144.66

O $23,604.80

O $26,399.13

Answer 1

First deposit = 1,000

After 4 years, this amount would be 1,000 * (1 + 0.08)^⁴ = 1,360.49

Half of it is withdrawn which is 680.24. This amount will be saved for 11 more years whose future value would be 680.24 * (1 + 0.08)^¹¹ = 1,586.08

Future value of deposit can be calculated as: [Deposit * (1 + Rate of Interest)^^Year]

Year	Deposit made	Money withdrawn	Money saved for years	Future value
1	1000
2	-
3	-
4	-	680.24		1586.08
5	-
6	2000		9	3998.01
7	2000		8	3701.86
8	2000		7	3427.65
9	2000		6	3173.75
10	2000		5	2938.66
11	2000		4	2720.98
12	2000		3	2519.42
13	2000		2	2332.80
14	-		1
15	-		0
				26399.20

At the end of year 15, 26,399.20 can be withdrawn. Option D is correct.