SOLUTION: Determine the interest earned of a 12-year investment with an interest rate of 5.3 %/a compounded weekly, if future value is $41800. A) $ 17 630.77 B) $ 356.07 C) $ 14404.36 D)

Algebra ->  Finance -> SOLUTION: Determine the interest earned of a 12-year investment with an interest rate of 5.3 %/a compounded weekly, if future value is $41800. A) $ 17 630.77 B) $ 356.07 C) $ 14404.36 D)      Log On


   

Question 1102512: Determine the interest earned of a 12-year investment with an interest rate of 5.3 %/a compounded weekly, if future value is $41800.
A) $ 17 630.77 B) $ 356.07 C) $ 14404.36 D) $19 663.67
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


If the initial amount is A, then the amount after 12 years, compounded weekly (52 times a year), with an annual interest rate of 5.3%, is

A%281%2B%28.053%2F52%29%5E%2812%2A52%29%29+=+A%2A1.8883

Given that the future value is $41800, the original amount is
A%2A1.8883+=+41800
A+=+41800%2F1.8333+=+22136.33

The original amount is $22136.33; the future value is $41800; the interest is
41800-22136.33+=+19663.67

Answer D.

Note there is a faster way to get to the interest amount, after we find that
A%2A1.8883+=+41800

In that equation, A*1 is the original amount; A*0.8883 is the interest. So the fraction of the total future value of $41800 that is interest is 0.8883/1.8883. So the amount of interest is
41800%2A%280.8883%2F1.8883%29+=+19663.67