The number of days is 6 approximately.
Explanation:
Given:
Principal, p = $100,000
Rate of interest, r = 0.9%
Annual Interest, I = $5000
Interest is Compounded daily
Time, t = ?
We know,
[tex]I = P [ ( 1 + \frac{r}{365} )^ 3^6^5^ X^ t - P[/tex]
[tex]I = 1000000 (1 + \frac{0.009}{365} )^3^6^5^t - 1000000\\\\I = 1000000 [ (1 - (1 + \frac{0.009}{365} )^3^6^5^t)]\\\\I = 1000000( 1 - (1.00002)^3^6^5^t)\\\\\\[/tex]
If compounded annually and t = 1 year
then
Daily interest = $904
Total Interest = $5000
Number of days = Total interest / daily interest
n = [tex]\frac{5000}{904}[/tex]
n = 5.53
Therefore, number of days is 6 approximately.
