Question

Ling has saved $73,700.00. If she decides to withdraw $2,819.00 at the beginning of every month and interest is 11.25% compounded quarterly, for how long can she make​withdrawals? Express your answer in years and months​ (from 0 to 11​ months).

Her last withdrawal will occur____ ​year(s) and____ ​month(s) from now.

​(Type whole​ numbers.)

Answer 1

Ling decided to withdraw at the beginning of every month = $2,819

Interest Rate = 11.25% compounded quarterly

Calculating Effective Annual Rate(EAR) :-

where, r = Interest Rate = 11.25%

m = no of times compounding in a year = 4 (Quarterly)

EAR = 11.7336%

now, with EAR we will calculate APR with monthly compounding:-

where, r = Interest Rate

m = no of times compounding in a year = 12 (Monthly)

EAR = 11.7336%

TAKing 12-root on both sides,

1.0092884574 = (1+r/12)

0.0092884574 = r/12

r = 11.1461%

So, APR with monthly compounding is 11.1461%

Calculating the No of Months Ling can make withdrawal:-

Where, C= Periodic Withdrawal = $2819

r = Periodic Interest rate = 11.1461%/12 = 0.928841666%

n= no of periods

Present Value = $73,700

Taking Log on both sides,

Solving Log with financial Calculator,

-0.1195304175 = -n*0.0040152890

n = 29.77 months or 2 years & 6 months

So, Her last withdrawal will occur 2 ​year(s) and 6 ​month(s) from now.