Question

Peoples Bank offers 8% compounded continuously on CDs What amount invested now grow to 100,000 in 25 years Hint the continuous compounding formula

Answer 1

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:

$A=Pe^{rt}$

Where, A is amount, P is principal, r is the rate of interest and t is the number of years.

Putting $A=100000, r=0.08, t=25$ in the above formula, we get

$100000=Pe^{0.08(25)}$

$100000=Pe^{2}$

$\dfrac{100000}{e^{2}}=P$

$\dfrac{100000}{7.389056}=P$

On further simplification, we get

$P\approx 13533.528$

Therefore, the amount 13533.528 is invested.