Question

Assume that you just invested $10,000 in a savings account paying 2 % interest compoundedcontinuously. 025 (20) A) How much will your investment be worth in 20 years?P)0 B) How long will it take your investment to double?

Answer 1

amount is $14918.25

after 34.65 year investment will be double

Explanation:

principal = $10000

rate = 2% = 0.02

to find out

How much will your investment be worth in 20 years

and How long will it take your investment to double

solution

we know the Continuously Compounded Interest formula i.e.

amount = principal
`e^(rt)` .................1

put the value amount , time 20 year for 1st problem and rate in equation 1

here rt = 0.02 × 20 = 0.4

we get amount

amount = 10000 ×
`e^(0.4)`

amount = 14918.25

so amount is $14918.25

and in 2nd part we put amount double of principal and rate to find out time in equation 1 so

amount = principal
`e^(rt)`

20000 = 10000
`e^(0.02t)`

2 =
`e^(0.02t)`

take ln both

ln
`e^(0.02t)` = ln 2

0.02 t = ln 2

t = ln 2 / 0.02

t = 34.657359

so after 34.65 year investment will be double