Finite Mathsection 5.2 Compound InterestCompound Interest Formula A = P P 1 + = 1 + irmmt n† where A = account value at time t years, t = time (in years), P = principle, m = (annual) compounding frequency = # times compounded each year, r = (annual) interest rate, i = = periodic interest rate, n = (m t) = # periodsrm†Ex1, Let the principle be $1000. Find the account value at the end of 2 years at annual interest rate 6% (a) compounded annually (b) compounded semiannually (c) compounded quarterly (d) compounded monthlyEx2, $200 is deposited every month where the first payment was made on May 30, 2002. Second payment was deposited on June 30, 2002, and so on. The last payment will be deposited on Dec 30, 2010. Account is compounded monthly at an annual interest rate of 6%.(a) How many deposits are there?(b) Find the future value (on Dec 30, 2010) of $200 deposited on May 30, 2002. (payment #1)(c) Find the future value (on Dec 30, 2010) of $200 deposited on June 30, 2002. (payment #2)(d) Find the future value (on Dec 30, 2010) of $200 deposited on Sep 30, 2005. (payment # )(e) Find the future value (on Dec 30, 2010) of $200 deposited on Nov 30, 2010. (payment # )(f) Find the future value (on Dec 30, 2010) of $200 deposited on Dec 30, 2010. (payment # )Def Effective Rate = = = 1A(1) A(0)A(0) P P P1 + rmrmmm1 + Ex3, Let the principle be $20000. Find the account value at the end of 5 years at annual interest rate 12% (a) compounded annually (b) compounded semiannually (c) compounded quarterly (d) Find the effective rate in each of the above case.Ex4, $500 is deposited every month where the first payment was made on March 30, 2003. Second payment was deposited on June 30, 2003, and so on. The last payment will be deposited on Dec 30, 2007. Account is compounded quarterly at an annual interest rate of 8%.(a) How many deposits are there?(b) Find the future value (on Dec 30, 2007) of $500 deposited on March 30, 2003. (payment # 1)(c) Find the future value (on Dec 30, 2007) of $500 deposited on Junce 30, 2003. (payment # 2)(d) Find the future value (on Dec 30, 2007) of $500 deposited on June 30, 2005. (payment # )(e) Find the future value (on Dec 30, 2007) of $500 deposited on Dec 30, 2007. (payment # )(f) Express the future value (value on Dec 30, 2007) of the account as a sum of future values of each deposit. That is, each term must be a future value of one deposit. (Write first 3 terms, +….+, and the last 3 terms.)(g)* Find the future value in a concise numerical expression.(In other words, find the sum in (d), final calculation is not