Question

In: Finance

Mr. Jones wishes to establish a fund for his newborn child’s education. The fund pays $60,000...

Mr. Jones wishes to establish a fund for his newborn child’s education. The fund pays $60,000 on the child’s 18th, 19th, 20th, and 21st birthdays. The fund will be set up by the deposit of a fixed sum on the child’s 1st through 17th birthdays. The fund earns 6 percent annual interest.

A) What is the required annual deposit.

B) What would the annual payments be, if the tuition fees in the above example are $60,000, $67,000, $75,000 and $83,000, respectively, for the four years involved?

Solutions

Expert Solution

Given Information:

Fund pays Annuity of $60000 for 4 years starting from Age - 18th

Annuals deposits from 1st to 17 Age

Rate of return = 6%

A) What is Annual deposit required?

First Calculate the Value of Future annuities at time 17.

= 56603.77358 + 53399.78640 + 50377.15698 + 47525.61979

Value of Annuities at Time 17 = 207906.3368

Now Calculate annual contribution required

FV = Annuity + Annuity x Cumulative Future value annuity factor @6% for 16 periods.

[ For cumulative Future value factor refer the tables or you can calculate as it is sum of (1.06)+ (1.06)² + ............. + (1.06)¹⁶ ]

207906.3368 = Annuity + Annuity x 27.21287967

207906.3368 = Annuity (1 + 27.21287967)

Annuity = 207906.3368 / 28.21287967

Annuity = 7369.19943

Annual Deposit required = $7369.1994 approx

2. Calculate again with different cash flows as 60000,67000,75000,83000.

First Calculate the Value of Future annuities at time 17.

= 56603.77358 + 59629.76148 + 62971.44623 + 65743.77405

Value of Annuities at Time 17 = 244948.7553

Now Calculate annual contribution required

FV = Annuity + Annuity x Cumulative Future value annuity factor @6% for 16 periods.

[ For cumulative Future value factor refer the tables or you can calculate as it is sum of (1.06)+ (1.06)² + ............. + (1.06)¹⁶ ]

244948.7553 = Annuity + Annuity x 27.21287967

244948.7553 = Annuity (1 + 27.21287967)

Annuity = 244948.7553 / 28.21287967

Annuity = 8682.160707

Annual Deposit required = $8682.1607 approx

jeff jeffy answered 1 year ago

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