Question

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 1

Let the principal amount she sets aside 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 times the interest is compounded
As compounding is done each day,  n = 365 times in one year * 35 years

$n = 365 * 35 = 12,775 \\ \\ Maturity\ Amount = \ 1,200,000 = P (1 + \frac{r}{100} )^n \\ \\ = P (1+\frac{0.016438}{100})^{12775} = 1.00016438^{12775}\ P \ \ = 8.1644\ P \\ \\ So\ P =\frac{ \ 1,200,000}{ 8.1644} = \ 146, 979.57$

She must set aside now $ 146, 979.57 in the bank, at 6% per annum compounded daily to receive $1,200,000 after 35 years when she retires at an age of 65 years.