Answer to Question #311751 in Finance for Ghhhh

Question

You need a P40,000 per year for 4 years to go to college. Your father invested P50,000 in a 7% account for your education when you were born. If you withdraw the P40,000 at the end of your 17th, 18th, 19th, and 20th years, how much money will be left in the account at the end of your 21st year?

Answer 1

The amount invested (P) = 50000

Amount to be withdrawn per year (A) =40000

Interest rate (i) = 7%= 0.07

The number of years (n) =21

Let the amount at time 0 be P₁

Let the amount at time 21 be A₁

Let the amount withdrawn in the 20th year be A₂

Let the amount withdrawn in the 21st year be A₃

A₁ $= P_1(1+i)^n$

$= 50000(1+0.07)$²¹

$=207028.1187$

$A_2=$ $\frac{A[(1+i)^n-1]}{i}$

$=​ \frac{40000[(1+0.07)^4 -1]}{0.07}$

$=$ 177597.72

$A_3 = A_2(1+i)$

$= 177597.72(1+0.07)$

$=190029.5604$

Amount of money left in the account $=A_1 -A_3$

$=207028.1187-190029.5604$

$=16998.55834$

The amount of money that will be left at the end of the 21st year will be approximately P16998.56