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)`

`(100000)/(e^(2))=P`

`(100000)/(7.389056)=P`

On further simplification, we get

`P\approx 13533.528`

Therefore, the amount 13533.528 is invested.