how much money must one invest at 4.25% compounded quarterly to have $8000 at the end of 5 years?

Question

anonymous · Answer

A formula for calculating annual compound interest is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$Where,
    A = final amount
    P = principal amount (initial investment)
    r = annual nominal interest rate (as a decimal)
    n = number of times the interest is compounded per year
    t = number of years
 In your case A=8000; r=.0425; n=4; t=5; P=______?
$$8000=P \left( 1+.0425/4 \right)^{4*5}$$$$P=\frac{8000}{(1.010625)^{20}}=$6475.738$$

anonymous · Answer

Many thanks, in what cases would I have to use a natural log in this problem?

anonymous · Answer

Under continuously compounded inerst the formula becomes$$A=Pe^{rt}$$where e is the base of the natural log

anonymous · Answer

clarification: in the case of continously compounded, why couldnt I divide A/(e^rt) to get my P?

anonymous · Answer

You could; e^rt takes the place of the (1+r/n)^nt in the case of discrete compounding; in your original problem, i divided by (1+r/n)^nt, but if the problem was posed as having continuously compounded interst, then i would have divided by e^rt

anonymous · Answer

Under continuously compounded interest P = $6468.423

anonymous · Answer

ok, I just worked out this problem "How much must one invest at 3% compounded continously to accumulate to $7000 in 6 yrs?" and got $5846.88 as answer based on the principles you showed me, is this right?  thanks again