Question

Harrison is comparing two certificates of deposit, one at a local financial institution and the other at an online financial institution. The local institution offers a rate of 6% compounded annually while the online institution offers a rate of 6% compounded quarterly. If Harrison has a principal amount of $5,000, which institution offers the better deal, assuming he makes no further deposits or withdrawals? Explain.

Answer 1

The online institution offer is the better deal

Step-by-step explanation:

The formula for compound interest, including principal sum is:

$A=P(1+\frac{r}{n})^{nt}$ , where

• A is the future value of the investment/loan, including interest
• P is the principal investment amount  
• r is the annual interest rate (decimal)
• n is the number of times that interest is compounded per unit t
• t is the time the money is invested or borrowed for

The local institution

∵ The local institution offers a rate of 6% compounded annually

∴ r = 6% = 6 ÷ 100 = 0.06

∴ n = 1 ⇒ compounded annually

∵ Harrison has a principal amount of $5,000

- Substitute them in the formula above

∵ $A=5000(1+\frac{0.06}{1})^{(1)t}$

∴ $A=5000(1.06)^{t}$

Let us find A for t = 1 , 2 , 3 , 10

∵ t = 1

∴ $A=5000(1.06)^{1}=5300$

∵ t = 2

∴ $A=5000(1.06)^{2}=5618$

∵ t = 3

∴ $A=5000(1.06)^{3}=5955.08$

∵ t = 10

∴ $A=5000(1.06)^{10}=8954.24$

The online institution

The online institution offers a rate of 6% compounded quarterly

∴ r = 6% = 6 ÷ 100 = 0.06

∴ n = 4 ⇒ compounded quarterly

∵ Harrison has a principal amount of $5,000

- Substitute them in the formula above

∵ $A=5000(1+\frac{0.06}{4})^{4t}$

∴ $A=5000(1.015)^{4t}$

Let us find A for t = 1 , 2 , 3 , 10

∵ t = 1

∴ $A=5000(1.015)^{4}=5306.82$

∵ t = 2

∴ $A=5000(1.015)^{8}=5632.46$

∵ t = 3

∴ $A=5000(1.015)^{12}=5968.09$

∵ t = 10

∴ $A=5000(1.015)^{40}=9070.09$

By comparing the amount of the future values in both offers we find that the future values of the online institution is greater than the future values of the local institution for the same number of years

∵ $(1.015)^{nt}$ > $(1.06)^{t}$

∴ The future value of the online institution > the future value of

    the local institution

The online institution offer is the better deal

Learn more:

You can learn more about the interest in brainly.com/question/12773544

#LearnwithBrainly