A trust fund will pay you $1200 per month for life once you turn 18. You are currently 9. Interest rates are expected to be 4.12% compounded quarterly. What is the current value of your trust fund?
I'll have to assume a lot of things to answer this question
1. you turned 9 today
2. You will live forever
3. The interest rate is always 4.12% pa Compunded quarterly until you are 18 then compounded monthly for ever after.
4. After you turn 18 your payment of $1200 will be at the end of each month
5. Your trust fund is never added to.
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quarterly interest rate = 0.0412/4 = 0.0103
monthly interest rate = 0.1012/12 = 0.003433333333...
once you get to 18 your payments will be the interest and nothing more otherwise the payments can't last forever
so let the amount you have in the fund at 18 be Xdollars
1200 = 0.00343333333...* X
X = $349514.56 (to the nearest cent)
Now the compound interest formula is S = P (1+i) n
where S is the future value = X = $349514.56
P is the principle(what you have to start with) = that is what we are trying to find
i is the interest rate for the compounding period = 0.0103
n is the number of compounding periods = 9years* 4 = 36 quarters
$349514.56 = P * 1.0103 36
$349514.56 / 1.0103 36 = P
P = $241686.60
The current value of your trust fund is $241686.60
+118653 
