Question

Math201:

Directions: Annual Percentage Yield (APV). Find the annual percentage yield (to the nearest 0.01%) in each case.

1.) A bank offers an APR of 3.2% compounded monthly.

Directions: Continuous Compounding. Use the formula for continuous compounding to compute the balance in each account after 1,5, and 20 years. Also, find the APY for this account.

1.) A $2,000 deposit in an account with an APR of 3.1%

Answer 1

Answer:- We have to find the annual percentage(to the nearest 0.01%)

1.)A bank offers an APR of 3.2% compounded monthly.

here, r =3.2% =0.032 , n=12(monthly)

APY = [1 + ( 0.032/12)]¹² - 1 = 0.032473534 = 3.24%

APY= 3.24%

Continuous Compounding : Using the formula for continuous compounding to compute the balance in each account after 1,5, and 20 years. Also, find the APY for this account.

1.)A $2,000 deposit in an account with an APR of 3.1%

For the Annual percentage Yield for continuous compounding (APY) = e^r-1

Here , r = 3.1% 0.031

APY = e^0.031-1 = 3.14%

Use the formula for determine future value when compounded continuously FV = PV e^rt

where PV is present value

FV is future value

r is rate of interest compounded

and t is time in years

PV = $ 2000 , APY = 3.14% = 0.0314

Now find balnce after 1 year

FV = 2000 e(0.0314)(1) = $ 2063.79

Now find balance after 5 years

FV = 2000e(0.0314)(5) = $10318.98

Now find balance after 20 years

FV = 2000e(0.0314)(20)  = $ 41275.92