Question

Sophia plans to invest $1,000 in each of three banks.

Bank A offers an annual interest rate of 12%, compounded annually.
Bank B offers an annual interest rate of 12%, compounded quarterly.
Bank C offers an annual interest rate of 12%, compounded monthly.
a. Write the function that describes the growth of investment for each bank in nn years.
b. How many years will it take to double her initial investment for each bank? (Round to the nearest whole
dollar.)
C.Sophia went to Bank D. The bank offers a "double your money" program for an initial investment of $1,000 in
five years, compounded annually. What is the annual interest rate for Bank D?

Answer 1

14.87%

Explanation:

For compound interest amount at the end, we have formulae as

a) annually ..
`P(1+r)^n` where n is the no of years

quarterly ..
`P(1+0.5r)^(2n)`

Monthly ..
`P(1+(r)/(12) )^(12n)`

b) Equate The formula there with P = 1000 to 2000

annually
`1000(1.12)^n =2000\\n = 6.15`

In apprxy 6 years and 2 months

Semi annually
`1.06^(2n) =2\\n = 5.95`

Or in 5 years 9 months

Quarterly

`1.03^(4n) =2\\n=5.875`

C) In 5 years the money becomes double

i.e.
`1000(1+r)^5 =2000\\1+r = 1.14870\\r=14.87%`