Show the steps 5 35 points The interest rate for the first t

5) (35 points) The interest rate for the first two years is 10% per year compounded annually. The interest rate for the third year is 12% per year compounded monthly. The last withdrawal depletes the fund. Find X. End of year 0 2 Cash flow $-3,000 SX SX SX

Solution

Balance in Beginning = 3000

Interest for 1st Year = 10%*3000 = 3000
Balance before Withdrawl of 1st Year = 3000+300=3300
Balance After Withdrawl of 1st Year = 3300 - X

Interest for 2nd Year = 10%*(3300-X) = 330 - 0.1X
Balance before Withdrawl of 2nd Year = (3300 - X) + (330 - 0.1X) = 3630 - 1.1X
Balance After Withdrawl of 2nd Year = (3630 - 1.1X) - X = 3630 - 2.1X

3rd year is of monthly compounding interest, so need to be calculted using FV = PV(1+r)ⁿ

Balance before Withdrawl of 3nd Year = (3630 - 2.1X)* (1 + 12%/12)¹²
Balance before Withdrawl of 3nd Year = (3630 - 2.1X)* 1.1268 = 4090.38 - 2.37X
Balance After Withdrawl of 3rd Year = (4090.38 - 2.37X) - X = 4090.38 - 3.37X

After 3 years funds got depleted, Thus it should be 0

4090.38 - 3.37X = 0
3.37X = 4090.38
X = 4090.38/3.37
X = 1215.08

$1,215.08