Question

An investors starts with a deposit of $1,430. After 2 months, she deposits an additional $170. 2 months later, she withdraws $130. 2 months after that, she withdraws an additional $370. One year after the initial deposit, the account has a balance of $1184.50. Estimate or approximate her dollar weighted return using the assumption that simple interest is earned and round your answer to the nearest 0.1%

Answer 1

First Deposit = 1,430$

Lets Take X as interest rate

Till Second Month Her interest would be 1430*X%*2/12

Her total Amount in account would be Interest + Deposit = 1430*X%*2/12 + 1,430

Then after two months she deposited additional amount of 170$

Total Amount of deposit would be 1430+170 = 1,500$

Till withdrawal Month from second deposit, Her interest would be 1500*X%*2/12

Total Amount in her account = 1500 + 1430*X%*2/12 + 1500*X%*2/12

She have withdrwan 130$ from her account , the deposit balance would reduce by 130$ that is 1500-130 = 1,370$

Interest on the above amount till next two months would be = 1370*X%*2/12

Total Amount in her account = Total Interest + Principle

=1430*X%*2/12 + 1500*X%*2/12 + 1370*X%*2/12 + 1370

She have withdrwan 370$ from her account , the deposit balance would reduce by 370$ that is 1370-370= 1,000$

Interest on the above amount till next year that is after 6 months (Because 6 months are already over) would be = 1000*X%*6/12

Total Amount in her account = Total Interest + Principle

=1430*X%*2/12 + 1500*X%*2/12 + 1370*X%*2/12 + 1000*X%*6/12 + 1000

It is given that total amount in her account = 1184.50

Therefore

1184.50 =  1430*X%*2/12 + 1500*X%*2/12 + 1370*X%*2/12 + 1000*X%*6/12 + 1000

1184.50-1000 = X%*{(1430*2/12) + (1500*2/12) + (1370*2/12) + 1000*6/12)

184.50 = X%*{238.33+250+228.33+500}

184.50 = X%*{1216.67)}

X% = 15.16%

Therefore Interest Would be 15.16%