Question

Need help solving this problem!!!A company will need $75,000 in 6 years for a new addition. To meet this goal, the company deposits money in an account today that pays 6% annual interest compounded quarterly. Find the amount that should be invested to total $75,000 in 6 years.
The company should invest $......

Here what I got but don't know if it's right.
I=Pe^rt
75,000=P^0.06*6
75,000=0.36

Answer 1

quarterly compounding not the same as continuous compounding

Answer 2

\[75,000=P(1+\frac{.06}{4})^{4t}\] solve for t

Answer 3

sorry that was wrong
\[75,000=P(1+\frac{.06}{4})^{24}\] solve for P

Answer 4

basically in one step
\[P=\frac{75,000}{(1.015)^{24}}\]

Answer 5

Could you show me step by step to this problem, so I know i'm doing it right. I have six more of these two do.

Answer 6

you are compounding quarterly, i.e. 4 times a year
formula for compouning n times a year with interest rate of "r" (as a decimal) is
\[P(1+\frac{r}{n})^{nt}\] where P is the principle and t is the time in years

Answer 7

in your case n = 4, r = .06 and t = 6 so we get a formula of
\[P(1+\frac{.06}{4})^{4\times 6}\] or
\[P(1.015)^{24}\]

Answer 8

since you knew you wanted to end with $75,000 and you want P you write
\[75,000=P(1.015)^{24}\] and solve for P