Use the formula for the compound interest with n compoundings each year to solve this problem. How long to the nearest tenth of a year will it take 12,500 to grow to 20000 at 6.5% annual interest compouned quarterly?

7.3 years.

Step-by-step explanation:

We are asked to find the time taken for 12,500 to grow to 20000 at 6.5% annual interest compounded quarterly. We will use compound interest formula to solve our given problem.  

, where,

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

Upon substituting our given values in above formula, we will get:

Now we will take natural log of both sides of equation as:

Using property , we will get:

Upon rounding to nearest tenth of year, we will get:

Therefore, it will take approximately 7.3 years for 12,500 to grow to 20000.

they are simplified

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have