Tomorrow, on your 25th birthday, you will receive the proceeds of a trust fund t
ID: 2618549 • Letter: T
Question
Tomorrow, on your 25th birthday, you will receive the proceeds of a trust fund that was set up by your wealthy grandmother. She invested $10 000 at 5% on your 5th birthday. You plan to invest your inheritance with an insurance company at a guaranteed rate of 12%. When you retire at the age of 55, you will begin to draw your investment in 20 equal installments calculated to reduce your fund to $0. You will make each withdrawal at the end of the year, and that the money that remains invested will continue to earn 8.5%
How much is in the bank today?
How much will be in the bank when you retire at age 65?
Assume you have $700,000 in the bank at age 65. What is the annuity payment over 20 years, you will draw for your retirement?
If inflation remains at 6% what will the amount be worth in today’s dollars?
Explanation / Answer
(a) The balance at the age of 5 years is $10000
It is invested at the interest @5%
Then balance at the age of 25 means after 20 years that is today is
= 10000 ( 1 + 0.05 )20 = 10000 ( 2.6533 ) = 26533$
The balance in bank after 40 years when retire at the age of 65 is
Interest on the amount invested after 20 years that mean today is 12%
Balance at the age of 65 = 26533 ( 1 + 0.12 )40 = 26533 ( 93.05 ) = 2468921.82$
Let also calculated at the age of 55 means after 30 years is
BAlance is = 26533 ( 1 + 0.12 )30 = 26533 ( 29.96 ) = 794928.68$
Answer 3. Let assume the balance in bank at the age of 65 is $700000
And we need amount in 20 equal installments in future
Then Interest amount earn of the money remain invested is 8.5%
let installment be X then
X* FVAF(8.5% , 20 years) = 700000
then X = 700000/5.112 = 136932 approx yearly installment
IF inflation is 6% then amount today in bank at the age of 25 is
26533(1+0.06)20 =26533 * 3.207 = 85094.92 approx