Given:
Rate of interest = 8% compounded continuously.
Amount = 100,000
Time = 25 years
To find:
The principal value.
Solution:
Formula for amount after continuous compound interest:
[tex]A=Pe^{rt}[/tex]
Where, A is amount, P is principal, r is the rate of interest and t is the number of years.
Putting [tex]A=100000, r=0.08, t=25[/tex] in the above formula, we get
[tex]100000=Pe^{0.08(25)}[/tex]
[tex]100000=Pe^{2}[/tex]
[tex]\dfrac{100000}{e^{2}}=P[/tex]
[tex]\dfrac{100000}{7.389056}=P[/tex]
On further simplification, we get
[tex]P\approx 13533.528[/tex]
Therefore, the amount 13533.528 is invested.
