Question

Lincoln invested $49,000 in an account paying an interest rate of 6\tfrac{1}{8}6

8

1

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% compounded daily. Eli invested $49,000 in an account paying an interest rate of 5\tfrac{5}{8}5

8

5

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% compounded continuously. After 20 years, how much more money would Lincoln have in his account than Eli, to the nearest dollar?

Answer 1

Using compound interest and continuous compounding, it is found that Lincoln would have $15,856 more in his account than Eli.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

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

In which:

• A(t) is the amount of money after t years.

• P is the principal(the initial sum of money).

• r is the interest rate(as a decimal value).

• n is the number of times that interest is compounded per year.

Hence, for Lincoln, we have that the parameters are as follows:

P = 49000, r = 0.06125, n = 365, t = 20.

Hence the amount will be of:

$A_L(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A_L(20) = 49000\left(1 + \frac{0.06125}{365}\right)^{365 \times 20}$

$A_L(20) = 166787$

What is continuous compounding?

The amount is given by:

$A(t) = Pe^{rt}$

For Eli, we have that r = 0.05625, hence the amount will be given by:

$A(t) = Pe^{rt}$

$A_E(20) = 49000e^{0.05625 \times 20} = 150931$

What is the difference?

It is given by:

$D = A_L(20) - A_E(20) = 166787 - 150931 = 15856$

Lincoln would have $15,856 more in his account than Eli.

More can be learned about compound interest at https://brainly.com/question/25781328