Question

a. If an account has an APR of 100 r % compounded continuously, its annual growth factor is

b. Based on your answer to part (a), the accounts t -year growth factor must then be

c.Based on your answers to parts (a) and (b), what is the account value after t years if P dollars is initially invested in the account?

d.Therefore, the function A that models the account's value after t years if interest is compounded continuously is (use the same parameter letters defined above):

Answer 1

Ans a.

If APR =r=100% with continuous compounding,

Annual Growth factor =e^100

Where e=2.7183 approx.

Ans b.

The Accounts t year growth factor will be =e^(rt)

Where e=2.7183 approx.

Ans c.

if P dollars initially invested, maturity amount after

t-years will be =P*e^(rt)

Where e=2.7183 approx.

Ans d.

the function A that models the account's value

after t years if interest is compounded continuously is

A=P*e^(rt)

Where e=2.7183 approx.

P=Initial $ investment