how much should alex invest?

Question

this is due at 12 tonight and i am dying -- this is my last problem and i would very much appreciate it if i understood how to do it lol

in 10 months, Alex will need $1290.00  to pay his college tuition. How much does he need to invest today into an account earning an  interest rate of 8.199% compounded monthly, so that he has enough money to pay his tuition?

Answer 1

The formula for compounding interest is as follows:

Total at the end of the Period= P(1 + r/n)^nt

Where P is the initial Principal invested

r=interest rate

n=number of iterations throughout the entire period (in this case, there are twelve months to the year)

t= the portion of the time period where you are compounding interest

plugging in our given numbers, we've got the following:

P= we are solving for P

r= 0.08199

n=12

t=10/12. This means out of 12 iterations over the year, you are interested in 10 months of that.

Total at the End of the Period= 1,290

So we have the following equation

1290=P(1+(0.08199/12))¹⁰

and we are solving for P

Doing some algebra, P =1290/(1+(0.08199/12))¹⁰

or P= $1,205.09