A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying 8% compounded quarterly at the time of your birth to yield $1,000,000 when you retire at age 59?
per quarter it is 0.08/4 = 0.02
so every quarter of a year multiply by 1.02
you get it during year 0 and during year 59 so for 60*4 quarters
= 240 quarters
so
1,000,000 = A * 1.02^240 = A * 115.89
A = 1,000,000/115.89
A = $ 8628.87
compounding is a marvel, but if you are getting 8% probably inflation is also happening.
To find out how much money your rich uncle must deposit in a trust fund, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $1,000,000)
P = Principal amount (the initial deposit we are trying to find)
r = Annual interest rate (8% or 0.08)
n = Number of times interest is compounded per year (quarterly means 4 times per year)
t = Number of years (from your birth until retirement, in this case, 59 years)
Now we can plug these values into the formula and solve for P.
1,000,000 = P(1 + 0.08/4)^(4*59)
First, let's simplify the exponent:
1.02^236
You may choose to calculate this using a calculator or a spreadsheet. In this case, it equals approximately 19.671.
So now we have:
1,000,000 = P(19.671)
To solve for P, divide both sides of the equation by 19.671:
P = 1,000,000 / 19.671
P ≈ $50,888.52
Therefore, your rich uncle would need to deposit approximately $50,888.52 in the trust fund at the time of your birth in order for it to grow to $1,000,000 by the time you retire at age 59.