Question

A couple have a 3-year-old child; they decided to make annual deposits into a savings account to fund his 4-year university education. With the first deposit being made on his fourth birthday and the last deposit being made on his 15th birthday. Then, starting on his 18th birthday, 4 withdrawals are required, starting at $3000 and increasing at a rate of 11%. If the effective annual interest rate is 6% during the whole period of time, what are the annual deposits in years 4 through 15?draw the cash flow diagram.

Answer 1

Solution :-

Value of Withdrawals at age of 15th =

= [ $3,000 / (1 + 0.06 )³ ] + [ $3,000 *(1+0.11) / (1 + 0.06 )⁴ ] + [ $3,000 *(1+0.11)² / (1 + 0.06 )⁵ ] + [ $3,000 *(1+0.11)³ / (1 + 0.06 )⁶ ]

= ( $3,000 * 0.839 ) + ( $3,300 * 0.792 ) + ( $3,663 * 0.747 ) + ( $4,065.93 * 0.705 )

= $10,736.29

Total Annual Deposit = 15 - 3 = 12

Now assume  annual deposit be X

= X * FVAF ( 6% , 12 ) = $10,736.29

X = $10,736.29 / 16.8699

X = $636.42

Therefire the Value of annual Deposit = $636.42

If there is any doubt please ask in comments

Thank you please rate