Finance questions

Question

1. You are a trust fund baby. Your trust fund is currently worth $1,234,000. The problem is the terms of the trust don’t allow you to receive any of the money until you are 27. You are now 21. The fund is earning 7.7% per year. How much will the fund be worth when you are 27 and too old to enjoy it?


2.You want to buy a car. To do so, you will need to take out a loan in the amount of $19,000. The longest you are willing to pay on the loan is five years. The interest rate on this type of loan is 5.0% per year.
How much will the equal monthly payments be?

3.You want to have $1,000,000 in 30 years. You already have $50,000. You think you can get a 7% annual return on your money. How much per year will you have to save to get to $1,000,000?

Answer 1

1.  At 21, it's worth $1234000.  At 22, it's worth $1234000 + 0.077*$1234000 = $1234000(1+0.077) = $1234000(1+0.077)^22-21.  Following this pattern, at 27 it's $1234000(1+0.077)^27-21.  You're never too old for that!

 

2.  $19000 = R(1-(1+0.050/12)^-5*12)/(0.050/12), by this amortization payment formula, where R is the monthly payment amount.

 

3.  I believe that if R is the yearly saving amount and each year you compound after saving, then the amount in the account goes from $50000 to $50000+R to ($50000+R)(1+0.07) =$50000(1+0.07) + R(1+0.07) in the first year, $50000(1+0.07)² + R((1+0.07)² + (1+0.07)) in the second year, and so on with a geometric series in 1+0.07, and after 30 years you solve $50000(1+0.07)³⁰ + R(1+0.07)((1+0.07)³⁰-1)/0.07 = $1000000.  Now if instead each year you compound before saving, you solve $50000(1+0.07)³⁰ + R((1+0.07)³⁰-1)/0.07 = $1000000, I believe.