compound interest

Question

Week 4 discussion problem # 1


1. How long will it take to double your money in an account paying 9%, compounded every other month? Round your answer to the nearest year and day. For example, 15 years and 6 days.

 

P 500 
A 1000


Hint:




A = P (1 + r/n)^ nt
A = 2P  double your money
2P = P (1 + r/n)^ nt

Need time 

Answer 1

Hello Sonia,

 

Using the formula you began working with...

2P = P (1+r/n)^nt

 

This is equivalent to

2 = (1+r/n)^nt

 

r = 9% = .09

n = 6 compounding every other month

 

2 = (1+.09/6)^6t

2 = 1.015^6t

 

This can be rewritten as

2 = 1.015⁶•1.015^t

2 = 1.09344 • 1.015^t

1.829 = 1.015^t

 

Take ln of both sides

ln 1.829 = t ln 1.015

.6038 = .01489 t

t = 40.5555

 

This equals 40 years 200 days using a 360 day year

Or 40 years, 6 months, 20 days