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You have $10,000 to put in one of the three accounts below. Find out how much each account would be worth after 10yrs then predict which account will give you the most money.
2.) By how much in dollars does the best account outperform the worst account (show work please)

Accounts
1. simple interest (rate=1.2%)
2. compound annually(rate=1.2%)
3. compounded monthly(rate=1.2%)

Sagot :

Answer:

1. 11,200

2. 11,266.92

3. 11,274.29

The best account outperformed the worst by $74.29.

Step-by-step explanation:

Interest Formulas

To calculate the amount of money in an account with simple interest, we use the simple interest formula

                                         [tex]A=P(1+rt)[/tex],

where P is the initial deposit, r is the rate (in decimal form), t is the time in years, and A is the value of the account after t years.

For compound interest, its formula is

                                         [tex]A=\left(1+\dfrac{r}{n}\right)^{nt}[/tex],

where A, r and t are the same variables as listed above and n is the number of times the interest is compounded per time period (usually it's annual).

[tex]\dotfill[/tex]

Solving the Problem

Question 1

We're told that

  • P = 10,000
  • t = 10
  • r = 0.012

1.

We need to use the simple interest formula to find our answer,

                     [tex]A=10000(1+(0.012)(10))=\boxed{11200}[/tex].

2.

We're need to use the compound interest formula. Since the interest compounds once a year, we can make n be in years (n = 1).

                         [tex]A=\left(1+\dfrac{0.012}{1}\right)^{(1)(10)}=\boxed{11266.92}[/tex]

3.

We use the compound interest formula, but since the interest compounds monthly and n is in years, n = 12 (once every month for every year).

                      [tex]A=\left(1+\dfrac{0.012}{12}\right)^{(12)(10)}=\boxed{11274.29}[/tex]

[tex]\dotfill[/tex]

Question 2

The best and worst account the problem refers too are the ones that generates the most and least amount of money by the end of the 10-year term.

The best in this case is account that has interest compounded monthly, the worst being the simple interest one.

So, to find how much the best made more than the worst we take their difference.

                                 11274.29 - 11200 = 74.29

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