Question

Gregory may choose between two accounts in which to invest $5000. Account A offers 2.3% annual interest compounded monthly. Account B offers continuous compound interest. Greg plans to leave his investment untouched (no further deposits and no withdrawals) for 10 years.
need help calculating account b's balance

Answer 1

Answer:

Gregory should take the continuos compound interest.

Step-by-step explanation:

If we calculate the Amount with both type of interest, we have:

Annual interest compounded monthly:

$A=P(1+\frac{r}{n} )^{nt} \\A=5000(1+\frac{0.023}{12} )^{12(10)} \\A=6291.61$

This means that with this interest, after 10 years he will get $6,291.61.

Continuous compound interest:

$A=Pe^{rt} \\A=5000e^{0.023(10)} \\A=6293$

Meaning that Gregory will get 6,293.

As you can see, it's not a big difference, only $2 more, but it's still better.

(Image attached are formulas with the variables meanings)