Question

Whitney deposits $9,000 for two years. She compares two different banks. State Banks will pay her 4.1% interest, compounded monthly. Kings Savings will pay her 4.01% interest, compounded continuously.

Answer 1

The student's question involves comparing compound interest rates and frequencies for two different banks, using specific formulas for each bank's interest computation.

Step-by-step explanation:

The student asked about the practical application of compound interest in saving money, considering different interest rates and compounding frequencies at two different banks.

For State Bank, which offers 4.1% interest, compounded monthly, the formula to use is A = P(1 + r/n)^(nt) where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial sum of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

For King's Savings, which offers a 4.01% interest rate compounded continuously, the formula used is A = Pe^(rt), where e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, t is the time the money is invested, and P is the principal amount.

Answer 2

1)state bank

2)$16.21

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW

Whitney deposits $9,000 for two years. She compares two different banks. State Banks will pay her 4.1% interest, compounded monthly. Kings Savings will pay her 4.01% interest, compounded continuously.Which bank pays higher interest? How much higher?

The Amount in the formula for compound interest is

A= P(1+r)^2

P = principal amount,

r = rate per periods,

t = number of periods,

To know the interest she got from the State bank, we say

P = $ 9000, r = 4.1% = 0.041, t = 2 years,

A= 9000(1+0.041)^2

A= 9000(1.041)^2

= 9767.74

Then interest earned = A - P

= 9767.74 - 9000

= $ 767.74

To know the interest she got from the State bank, we say

P = $ 9000, r = 4.01% = 0.0401, t = 2 years,

A= 9000(1+0.0401)^2

A= 9000(1.0401)^2

= 9751.53

Then interest earned = A - P

= 9767.74 - 9000

= $ 751.53

The difference between the two interest is ($ 767.74 - $ 751.53)

=$16.21

Hence state bank will have $16.21 higher interest