Compound interest a deposit of $400 is made in an account that earns interest at an annual rate of 2.5%. how long will it take for the balance to double when the interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously?

(a) annually = 28.07 years

(b) monthly = 27.75 years

(c) daily =  27.73 years

(d) continuously = 27.72 years

Step-by-step explanation:

given data

principal =  $400

annual rate = 2.5%  = 0.025

solution

we know here amount formula that is

amount = principal ×    ..................1

put here value for compound annually

800 = 400 ×

take ln both side

ln 2 = ln

t = 28.07 years

and

put value now in equation 1 for monthly

amount = principal ×

800 = 400 ×

take ln both side

ln 2 = 12t × ln(1.00208333)

t = 27.75 years

and

put value now in equation 1 for daily

amount = principal ×

800 = 400 ×

take ln both side

ln 2 = 365 t × ln (1.0000684932)

t = 27.73 years

and

for compound continuously

amount = principal ×   .................2

put here value

800 = 400 ×

t = 27.72 years

i think it’s c i believe