Final answer:
The woman will have $9,979.33 on deposit in the original bank after 11 years. If she deposits money in her brother-in-law's bank instead, she will have $8,877.69. Therefore, she would lose $1,091.64 over 11 years by using her brother-in-law's bank.
Step-by-step explanation:
(a) To find the final amount she will have on deposit, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (amount deposited each year)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Plugging in the values, we get:
A = 7000(1 + 0.03/1)^(1*11)
= 7000(1.03)^11
= 7000 * 1.4257619
= $9979.33
(b) To find the amount she will have if she deposits money in the bank paying 2% interest, we can use the same formula:
A = 7000(1 + 0.02/1)^(1*11)
= 7000(1.02)^11
= 7000 * 1.2682426
= $8877.69
(c) To find how much she would lose over 11 years by using her brother-in-law's bank, we can subtract the amount she would have in her brother-in-law's bank from the amount she would have in the original bank:
9979.33 - 8877.69 = $1091.64