# Thread: Find compounding interest & other problems

1. ## Find compounding interest & other problems

Hey all I'm completly new to this site and I have to say I am truly thrilled to find such a community. Here are my questions:

1. A painting purchased in 1998 for $75,000 is esitmated to be worth v(t)= 75,000e^t/5 dollars after t years. At what rate will the painting be appreciating in 2003? In 2003, the painting will be appeciaiting at$____ per year.

2. Let P(t) be the population (in millions) of a certain city t years after 1990, and suppose thta P(t) satisfies the differential equation P'= .02(t), P(0)= 7.

a. Find the formula for P(t)

b. What was the initial popluation in 1990?

c. What is the growth constant?

d. What was the population in 2000?

e. Use the differential equation to determine how fast the population is growing when it reaches 8 million people.

f. How large is the population when it is growing at the rate of 190,000 people per year?

3. Suppose that an investment grows at a CONTINUOUS rate of 9% rate each year. In how many years will the value of the investment double?

2. ## Re: Find compounding interest & other problems

We can't tell where you're stuck. Please show your work.Is this homework?

3. ## Re: Find compounding interest & other problems

A=P(1+r/n)^nt
A=amount
P=principal
r=rate
n=number times interest is calculated per year
t=number of year

Oh ya you also need the formula A=Pe^rt

7. ## Re: Find compounding interest & other problems

I came up with the 20% interest well 19.6%, anyhow I am stumped on the per year part?

8. ## Re: Find compounding interest & other problems

Originally Posted by Dmaze1003
Suppose that an investment grows at a CONTINUOUS rate of 9% rate each year.
In how many years will the value of the investment double?
Formula for future value (continuous compounding) : A[e^(i*t)]
At 9%, when does $1 accumulate to$2?
1[e^(.09t)] = 2
.09t = LOG(2)
t = LOG(2) / .09 = 7.7016... about 7 3/4 years ; OK?