# Allison is 30 years old and plans to retire at age with 1,200,000 in her retirement account. what amount would she have to set aside now in an investment paying 6% annual interest if the compounding is done daily

Answer:   Let the principal amount she sets a side in an investment be \$ P

She retires at an age of 65 , that is , in 35 years from the date of investment .

Period of investment = 35 years

rate of interest =6% per annum =( 6/365)% = 0.016438 % per day

r = 0.016438%

n= number of time the interest is compound

As compounding is done each day ,  $\\ n=(365\times 35)=12775$

Maturity Amount = 1,200,000\$ =P

⇒    = $\\ P(1+ 0.016438/100)^12775=(1.00016438)^12775$

P= \$1200000/8.1644=14697\$

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