Question

A principal amount of $2,500 is placed in a savings account with an APR of 4.1% compounded semi-annually for 7 years. The same principal amount is placed in a savings account with an APR of 2.2% compounded continuously for 10 years. Which account earns more interest?

The semi-annually compounded interest account earns more, with $615.19 in total interest earned.
The continuously compounded interest account earns more, with $821.41 in total interest earned.
The semi-annually compounded interest account earns more, with $821.41 in total interest earned.
The continuously compounded interest account earns more, with $615.19 in total interest earned.

Answer 1

ok did u use the site that the other user gave u to help me

Answer 2

oops i met You

Answer 3

I'm trying but it says apr not interest rate..unless their the same thing

Answer 4

hmm @axie can u help again

Answer 5

Hold Please

Answer 6

alrighty, are you comfortable using a calculator to solve?

Answer 7

I believe so

Answer 8

\[2500 (1.02) ^14\]

Answer 9

sorry the 14 is weird format, but its squared by 14 i believe

Answer 10

Oh that's fine, my calculator just doesn't seem to have a squaring thing on it

Answer 11

okay let me see what i can do on my end

Answer 12

Okay it seems, 2500 (1+interest semi(meaning 2)annually(year)) Squared by years

Answer 13

soo 2500 (1.02) Squared by 14 because the 7 would be annually and we have semi so 7*14, equalling 3298.697

Answer 14

but they want us to deicde which makes more, so let me try the 2nd one

Answer 15

To compare the two savings accounts, we can utilize the formula for compound interest:

For the semi-annually compounded account:

\[
A_{\text{semi-annual}} = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
\(A_{\text{semi-annual}}\) = the future value of the investment/loan, including interest
\(P\) = the principal investment amount (the initial deposit or loan amount) = $2,500 in both cases
\(r\) = the annual interest rate (decimal) = 4.1% or 0.041 for the semi-annually compounded
\(n\) = the number of times that interest is compounded per year = 2 for semi-annually compounded
\(t\) = the time the mazuma is invested or borrowed for, in years = 7 years for the semi-annually compounded

Now, let's calculate the future values for both accounts:

\[
A_{\text{semi-annual}} = 2,500 \left(1 + \frac{0.041}{2}\right)^{2 \cdot 7} \approx \$2,974.27
\]

For the perpetually compounded account:

\[
A_{\text{continuous}} = 2,500 \cdot e^{0.022 \cdot 10} \approx \$3,161.84
\]

Now, let's calculate the interest earned for both accounts:

\[
\text{Interest}_{\text{semi-annual}} = A_{\text{semi-annual}} - P = \$2,974.27 - \$2,500 = \$474.27
\]

\[
\text{Interest}_{\text{continuous}} = A_{\text{continuous}} - P = \$3,161.84 - \$2,500 = \$661.84
\]

So, the perpetually compounded interest account earns more with \$661.84 in total interest earned.

Answer 16

Well i guess try that LOL im sorry

Answer 17

I tried but I'm glad u were able to show the work

Answer 18

I have more questions 0-0

Answer 19

OH DEAR

Answer 20

i found a worksheet that shows it by hand but i was tryna calculate what the heck "e" was LOL

Answer 21

fair anyways onto the next

Answer 22

@kingsteve