If 3000 dollars is invested at interest, find the value of the investment...

Question

If 3000 dollars is invested at interest, find the value of the investment at the end of 6 years if interest is compounded a) annually  b) quarterly  c) monthly  d) continuously 

Answer 1

There was no stated interest rate so we will state the value of the investment for each of the time periods and then show an example assuming the interest rate is 5%:

Compounded Annually: 3000 x ( 1+ i )⁶ = 3000 x 1.05)⁶ = $4,029.29

Compounded Quarterly: 3000 x ( 1 + i/4 )²⁴ = 3000 x 1.05/4)²⁴ = $4,042.05

Compounded Monthly: 3000 x ( 1 + ii/12)⁷² = 3000 x 1.05/12)⁷² = $4,047.05

Compounded Continuously: 3000 x 3000 eⁱ⁶ = 3000 x e^.05x6 = $4,049.58

Answer 2

since I don't know what the interest rate is, in general

A(t) = P(1 + r/n)^nt

where P is the principal amount

r is the rate

n is the number of times per t that interest is compounded

t is time, usually in years

So, for this problem A(t) = 3000(1 + r/n)^nt

for part (a) n = 1 so, A(t) = 3000(1 + r)^t

for part (b) n = 4 so, A(t) = 3000(1 + r/4)^4t

for part (c) n = 12 so, A(t) = 3000(1 + r/12)^12t

for part (d) we take the limit as n approaches infinity and get A(t) = 3000e^rt

(e is the number e)

after you replace the interest rate for r, you can find A(6) to answer parts a-d