Question

Jim saw that other bank offered the same rates but compounded the interest more often. Consider if he still put $15,000 into a saving account for 5 years that provided 2.8% annually but compounded it in each of the following ways match the following:
Weekly-
Daily-
Continuously-
Monthly-
Semi-annually-
Quarterly-

Answer 1

Answer:

See Picture. I made a 100.

Step-by-step explanation:

Weekly- $17253.46

Daily- $17254.01

Continuously- $17254.11

Monthly- $17251.29

Semi-annually- $17237.36

Quarterly- $17245.69

Answer 2

Compound interest is the addition of interest on the interest of the principal amount.

What is compound interest?

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

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

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \ 17,253.46$

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \ 19,554.55$

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

$A = Pe^{rt}$

Substitute the values, we will get,

$A = 15000 \times (e^{0.024 \times 5})\\\\A= \ 16,912.45$

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \ 15211.23$

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \ 17,237.36$

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

$A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \ 17,245.7$

Learn more about Compound Interest:

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