math help please?

Question

Future value. If $50,000 is deposited in a bank account paying 5% compound quarterly, than what will be the value of the account at the end of 18 years? How long will it rake for the investment to double, compound quarterly? How long will it take for the investment to triple, compound continuously?
A=P(1+(r/n))^nt

how do I solve this problem. please show how you got it.
thank you.

Answer 1

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

1. A = 50000 [ 1 + (.05/4) ]^ (4*18) = 50000 [ 1.0125 ]^72 = 122,296.01

2. 100000 = 50000 [ 1.0125 ]^4t
2 = 1.0125^4t
log 2 = 4t * log 1.0125
log 2 / log 1.0125 = 4t
55.8 = 4t
13.95 years = t

3. A = Pe^(rt)
150000 = 50000 e^(.05t)
3 = e^(.05t)
ln 3 = .05t
21.97 = t
22 years

Answer 2

To simplify things, set it up as
(A/P) = [ 1+(r/n)]^(nt)
This way, you can do the double and triple problems. r= 0.05, n=4 and t=18. So you will have
(A/P) = [1.0125]^72 for the first problem. For the others, you know (A/P) and you solve for n*t.
Your best bet for calcs is logarithms. Then for the first problem Log(A/P)= 72*Log(1.0125).
For the others, you know A/P=M, so the equation to solve is Log(M)= (n*t)*Log(1.0125)

Answer 3

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

A = final amount
P = initial amont
r = rate
n = compounding
t = time in years

plug in chunks
A = 50,000 (1 + .05/4)^(4*18)
A = 50,000 (1.0125)^72
A =~ $122,296.01


the final amount is 50,000 x 2 = 100,000

100,000 = 50,000 (1 + .05/4)^(4t)
2 = (1.0125)^(4t)
log2 = 4t log1.0125
4t = log2 / log1.0125
t = log2 / (4log1.0125)
t =~ 13.95 years


the formula for compounding continously is:
A = Pe^(rt)

50,000 = 150,000

150,000 = 50,000e^(.05t)
3 = e^(.05t)
ln3 = .05t
t =~ 21.97 years