. On Qiya’s 1st birthday, a savings account was opened for her containing $10,00
ID: 2761897 • Letter: #
Question
. On Qiya’s 1st birthday, a savings account was opened for her containing $10,000. By her 5th birthday, the account had grown to $13,500 and $1000 was added. By her 13th birthday the account had grown to $17,000 and $2000 was added. On her 16th birthday, she withdrew $5,000 to buy a car, leaving a balance of $15,000. On her 18th birthday, the account contained $16,500 which she will use for college. No other deposits or withdrawals were made. Use the time-weighted method to calculate the effective annual yield rate over the seventeen-year period.
Explanation / Answer
Return in 1st period(lasting for 4 years) = (13500-10000)*100/10000=35%
Return in 2nd period(lasting for 8 years) = (17000-(13500+1000))*100/(13500+1000)=17.24%
Return in 3nd period(lasting for 3 years) = ((15000+2000)-(17000+2000))*100/(17000+2000)=-10.23%
Return in 4nd period(lasting for 2 years) = (16500-(15000))*100/(15000)=10%
TWRR = (((1+return period1)*(1+return period2)*((1+return period3)*(1+return period4))^(1/total years)-1)*100
=(((1+0.35)*(1+.1724)*(1-.1023)*(1+.1))^(1/(18-1))-1)*100 = 2.66%
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