Question

6000 for 6 years at 81/2 % compounded daily will grow to a) $9.990.02 b)9.060.00 c) 9788.81 d)9991.15

Answer 1

Answer:

d)9991.15

Step-by-step explanation:

We have a sum of money ($6000) compounded daily at an annual interest rate of 8.5% for 6 years.

If the interest is compound daily, and we take a m=365 days a year (or 365 subperiods m), the daily nominal interest rate is:

$i_d=\dfrac{i}{m}=\dfrac{0.085}{365}=0.000232877$

Then, we can express the final valueo of $6000 compounded daily at an annual interest rate of 8.5% for 6 years as:

$FV=IV\left(1+\dfrac{i}{m}\right)^{n\cdot m}\\\\\\FV=6000(1+0.000232877)^{6\cdot 365}\\\\FV=6000(1.000232877)^{2190}\\\\FV=6000\cdot1.665192322\\\\FV\approx9991.15$