Question

Use the compound interest formulas to solve. A = P(1 + r/n)nt and A = Pert Suppose you have $3000 to invest. Which investment yields the greater return over 10 years: Account 1: 6.5% compounded semiannually? Account 2: 6% compounded continuously? The account with the better investment is Account which yields dollars more after 10 years.

Answer 1

Answer:

Account 1 yields greater return.

Step-by-step explanation:

Lets solve for the first formula:

$A=P(1+\frac{r}{n} )^{nt}$

First, change 6.5% into a decimal:

6.5% -> $\frac{6.5}{100}$ -> 0.065

Now, plug in the values for Account 1:

$A=3,000(1+\frac{0.065}{2})^{2(10)}$

$A=5,687.51$

Now solve for Account 2:

Change 6% into a decimal:

6% -> $\frac{6}{100}$ -> 0.06

Now plug in the values:

$A=3,000e^{0.06(10)}$

$A=5,466.36$

Account 1 yields better money after 10 years.