Question

How long does it take to become a​ millionaire? A ​$500,000 investment will hit​ $1 million in 39 years at an annual interest rate of 1.79​%. How long will it take to become a millionaire if the annual interest rate increases to 2.34​%?

Answer 1

Answer:

It will take 30.10 year

Explanation:

We have given initial investment $500000

Future value = $ 1 million = $1000000

Rate of interest r = 1.79 %

We have to find the time taken to reach the amount $1000000

We know that future value is equal to $A=P(!+\frac{r}{100})^n$

$1000000=500000(!+\frac{1.79}{100})^n$

$2=(1.0179)^n$

Taking log both side

$log2=nlog1.0179$

n×0.0077 = 0.3010

n = 39.09 year

Now in second case rate of interest

r = 2.34 %

So $1000000=500000(1+\frac{2.34}{100})^n$

$2=(1+\frac{2.34}{100})^n$

$2=1.0234^n$

taking log both side

log 2 = n log 1.0234

n×0.01 = 0.3010

n = 30.10 year