Mathematics, 03.10.2019 03:30 ashleybashaam6821

$5,000 is deposited today into a bank account. the account earns 7.5% per annum compounded half yearly for the first 6 years, then 7.8% per annum compounded quarterly thereafter. assuming no further deposits or withdrawals are made,

(c) calculate the account balance 6.5 years from today.

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Answer from: jessica01479

The account balance 6 years from today is $8,082.44.

Step-by-step explanation:

This is a compound interest problem

The compound interest formula is given by:

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

In which A is the amount of money, 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 unit t and t is the time the money is invested or borrowed for.

In this problem, we have that

The total amount formula changes after 6 years, at which point each of the principal(initial money), interest rate, and n changes.

This exercise asks the account balance after 6.5 years. However, after years, some parameters change. This means that to find the balance after 6.5 years, first we have to find after 6 years, and then for the next half year, with the new parameters.

Step 1: Finding the balance after 6 years.

A is the balance, the value we have to find.

The loan is of $5,000. So P = 5,000 .

The account earns 7.5% per annum compounded half yearly, so r = 0.075, n = 2 .

We want to find the account balance in 6 years, so t = 6

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

$A = 5,000(1 + \frac{0.075}{2})^{12}$

A = 7,777.27

After 6 years, the balance is $7,777.27. Now, we compound this value for half a year, with the second definition.

Final step: Finding the balance after 6.5 years.

A is the balance.

The value that is going to be compounded is $7,777.27. So P = 7,777.27

7.8% per annum compounded quarterly, so r = 0.078, n = 3 .

This compounding is only going to be valid for 6 months. However, the time is measured in years, so t = 6

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

$A = 7,777.27(1 + \frac{0.078}{3})^{1.5}$

A = 8,082.44

The account balance 6 years from today is $8,082.44.

Answer from: Quest

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

Answer from: Quest

10 you would take 50/ .2

step-by-step explanation:

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