Having trouble with this problem, can you please help me?

Question

Suppose that you want to have to have $100,000 retirement fund after 30 years. How much will you need to deposit now if you can obtain an APR of 9.6%, compounded daily?(assume no additional deposits or wtihdrawals were made.)

Answer 1

about 5600 bucks, and it would be great to add to it.

Answer 2

Use the formula

A = P(1+r/n)^(nt)

where P is the initial amount, A is the final amount, r is the interest rate, t is time in years, and n is the number of times per year interest is compounded. We have A = 100,000, r = 0.96, t = 30, and n = 365.

You then have 100000 = P(1+0.096/365)^(10950).

Take the natural log of both sides, using 100000 = 10^5, gives you
5 ln 10 = 10950 ln (1+0.096/365) + ln P.

Solving for ln P gives you ln P = 7.9135, so P = $5615.60.

Answer 3

daily rate 9.6%/365 = 2.63013698*10-2%

p = 2.63*10^-4, x be the inital amount

x * (1.000263013698)^(365*30) = 100,000 ,

x = 5615.6

Answer 4

Just use compound interest formula

A = P(1 + r%)^t
where $A = amount at maturity = $100,000
$P = amount invested
r in interest paid in each term = 9.6%/365.25 per day
t = number of terms= 30*365.25days

So 100000 = P(1 + 0.096/365.25)^(30*365.25)

So P = 100000(1 + 0.096/365.25)^(-30*365.25)
= $5615.60 to nearest cent

Answer 5

9.6% compounded daily = 0.096/365.25 = 0.00026283/day
(365.25 is used to account for leap years)
[30*365.25] = 10957 days
A = P(1+i)^n
P = A/(1+i)^n
P = $100,000/(1.0006283)^10957
P = $5,616.34

There are many assumptions that will result in slightly different answers, e.g. 30 years could be 10,958 days

Answer 6

100,000 = Ao (1 + .096 / 365) ^ (30*365)

Solve for Ao

Ao = 100,000 / 17.81 = 5615 dollars

Answer 7

1.00 daily