5 points Leonard compounded monthly After two years he stop

5 points) Leonard ( compounded monthly. After two years, he stops the deposits. He does not deposit or withdraw any money for the next two years. From the fifth year (49th month), Leonard wishes to withdraw money every month for the next three years. How much money will Leonard be able to withdraw every month from the 49th month? deposits $700, every month, in a savings account that pays 12% per year,

Solution

P = M ( A-1) (q/i)

P = Principle amount to be earned after 2 years

M = regular deposit amount = 700

A = [ 1 + (i/q) ]^nq

q = compounded period = 12

i = intrest rate = 12% = 0.12

n = number of years = 2

A =   [ 1 + (0.12/12) ]^2x12

A = 1.27

P = M ( A-1) (q/i)

P = 700 x (1.27 - 1 ) x (12/0.12)

P = 18900

Amount after 24 months is 18900

Now the amount after the remaining 2 yrs

A = AMount

P = Principle = 18900

t = 2ys

i = 0.12

n = 12 months compounded monthly

A = P ( 1 + r/n)^nt

A = 18900 (1+ [0.12/12])^2x12

A = 24003$

So from 49th month leonard want to withdraw for next 36 months

i = 12/12 = 1%

Months withdrawel = 24003 (A/P,1%,36)

(A/P,i,n) = [i (i+1)ⁿ] [(i+1)ⁿ - 1]^-1

Months withdrawel = 24003  [0.01 (0.01+1)³⁶] [(0.01+1)³⁶ - 1]^-1

Months withdrawel = 797$