Question

Gabriella invested $73,000 in an account paying an interest rate of 3%
compounded continuously. Mila invested $73,000 in an account paying an interest
rate of 3% compounded quarterly. After 5 years, how much more money would
Gabriella have in her account than Mila, to the nearest dollar?

Answer 1

Answer:

Gabriella will make $61 more than Mila after 5 years

Step-by-step explanation:

Gabriella Data

Principal Amount P= $73,000

Rate r = 3% or 0.03

Compounded continuously

Time t = 5 years

The formula used is: $A=Pe^{rt}$

Putting values and finding A

$A=Pe^{rt}\\A=73000e^{0.03*5}\\A=73000e^{015}\\A=84813.899\\A\approx84814$

So, After 5 years Gabriella will have $84814

Mila Data:

Principal Amount P= $73,000

Rate r = 3% or 0.03

Compounded quarterly n = 4

Time t = 5 years

The formula used is:$A=P(1+\frac{r}{n})^{nt}$

Putting values and finding A

$A=P(1+\frac{r}{n})^{nt}\\A=73000(1+\frac{0.03}{4})^{4*5}\\A= 73000(1+0.0075)^{20}\\A= 73000(1.0075)^{20}\\A=73000(1.161)\\A=84753$

So, After 5 years Mila will have $84753

Now subtracting to find the difference 84814-84753 = 61

So, Gabriella will make $61 more than Mila after 5 years