Suppose 1 050 is put in a money market account that pays an

Suppose $1, 050 is put in a money market account that pays an interest rate of 3.2 % a year. If interest is compounded semiannually, how much will be in the account in 4 years, 6 years and 8 years ? If interest is compounded continuously, how much will be in the account in 4, 6, 8 years ? If interest is compounded continuously, what is the doubling time ?

Solution

P = $ 1050 ; r = 3.2% = 0.032

a) A mount = P(1+ r/2)^2t

t = 4 yrs ; A = 1050(1 +0.032/2)^8 = $ 1119.11

t = 6 yrs ; A = 1050( 1+0.032/2)^12 = $ 1270.32

t = 8yrs ; A = 1050(1 +0.032/2)^16 = $ 1353.59

b) Compounded continously :

Amount = Pe^(r*t)

t = 4; A = 1050e^(0.032*4) = $ 1192.8

t = 6 ;A = 1050e^(0.032*6) = $ 1272.25

t = 8 ;A = 1050e^(0.032*8) = $ 1356.34

c) time for doubling :

2P = Pe^(0.032t)

2 = e^(0.032t)

take natural log on both sides : t = ln2/0.032 = 21.66 yrs