Question

the formula for compound intrest is given by A=P(1+r)^t where A is the total amount of money, P is the principalinvested, r is the intrest rate, and t is the time in years. If $5000 invested at 6.5% intrest compounded annually yields $25,000, for how many years was the money invested?

Answer 1

Given this equation
A=P(1+r)^t

how do you find t in terms of the other variables?

Answer 2

Well,
A/P = (1+r)^t

hence taking the natural log of both sides

ln(A/P) = ln( (1+r)^t )
= t . ln(1+r)

therefore

t = ln(A/P) / ln(1+r)

Answer 3

Now substitute all of your values of A, P and r and find t.

Answer 4

can you explain it

Answer 5

which step of the algebra don't you understand:


step 1: A/P = (1+r)^t

hence taking the natural log of both sides

step 2: ln(A/P) = ln( (1+r)^t )
step 3: = t . ln(1+r)

therefore

step 4: t = ln(A/P) / ln(1+r)

Answer 6

what does r equal

Answer 7

r is the interest rate 6.5%. As ever, you need to express that in decimal format. Hence
r = 0.065

Answer 8

so would i substitue like this. ln(5000)/ln(1+1.065)

Answer 9

Almost ln(A/P), not ln(P)

Answer 10

so ln(25,000/5000)/ln(1+0.065)

Answer 11

yes

Answer 12

is the answer 4.69