Question

An analyst wants to save $10,000 for a new car and currently has $8,000. If he invests the $8,000 at a 5.5% annual interest rate, how long will it take for this investment to reach $10,000?  

4.9 years

4.6 years

4.2 years

5.0 years

4.5 year

Answer 1

We have the equality, 10000 = 8000*1.055^n, where

n = the period for which the amount of 8000 should

be invested.

Solving for n,

10000/8000 = 1.055^n

1.25 = 1.055^n

Taking log of both sides

log1.25 = n*log1.055

n = log1.25/log1.055 = 0.09691/0.02325 = 4.16817

Answer: 4.2 years [when rounded off to 1 decimal]

VERIFICATION:

8000*1.055^4.2 = $10,017.29 [with rounding off to 1 decimal place]

With 4 decimal places rounding off: 8000*1.055^4.1682 = $10000.25