Question

Adam withdraws uniformly from a savings account, at a rate of $ 3 000 for 6 years. Then due to unforeseen circumstances, he needs to increase his annual withdrawal by an additional $ 1 900. He continues to withdraw money at this increased rate for another 5 years until the account is exhausted. With an interest rate of 10%, what was the initial value of the savings account?

Answer 1

As per the question the uniform withdrawal of $3000 made by Adam for 6 year

Annual withdrawal (A) =$3000

Period (N) =6 years

Rate of interest (i) = 10%

Present worth (PW) = A(P/A,i,N) = 3000(P/A,10%,6) = 3000(4.3553) =$13065.9

PW of withdrawn from year 1 to 6 = $13065.9

Due to some problem he increased his annul withdrawal by $1900 for another five year

A1=3000 + 1900 =4900

G=1900

N= 5 years

Rate of interest (i) = 10%

A=A1 + G(A/G,10%,5) = 4900 + 1900(1.8101) = $8339.19

Present worth (PW) of the withdrawal = 8339.19(P/A,10%5)(P/F,10%,6)

Present worth (PW) of the withdrawal = 8339.19(3.7908)(0.5645) = $17845.087

PW of withdrawn from year 7 to 11 = $17845.087

Initial value or PW of the saving account = PW of withdrawn from year 1 to 6 + PW of withdrawn from year 7 to 11

Initial value of the saving account (PW) = $13065.9 + $17845.087 = $30910.98

Initial value of the saving account is $30910.98