Suppose you deposit $ 1900 in an account with an annual interest rate of 6 % compounded quarterly. Use the formula A = P ( 1 + r n ) n t and round each answer to 2 decimal places, if necessary.

Question

Find an equation that gives the amount of money in the account after  years.

Find the amount of money in the account after years.

After years, there will be $ ___ in the account.

How many years will it take for the account to contain ?

It will take ___ years for there to be  in the account.

If the same account and interest were compounded continuously, how much money would the account contain after  years?

With continuous compounding interest, there would be $ ___ in the account after  years.

Answer 1

A=1900(1+.06/4)^4(5)

= 1900(1.015)^20=$2,559.02 afret 5 years with quarterly compounding

3800 = 1900(1.015)^4t

2 = 1.015^4t

log_1.0152 = 4t

t =(1/4)log_1.0152= .25ln2/ln1.015 =about 11.63888 years

= about 11 years 7 months 10 days to reach $3800 with same rate and compounding

with continuous compounding

A= 1900e^.06(5)=1900e^.3 =$2,564.73, just $5.71 cents more than quarterly compounding at end of 5 years with same interest rate