Answer: it would take 7 years more for Brianna's money to double than for Adam's money to double
Step-by-step explanation:
Considering Brianna's investment,
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = $480
r = 6.5% = 6.5/100 = 0.065
A = 2 × 480 = $960
Therefore,
960 = 1800 x 2.7183^(0.065 x t)
960/1800 = 2.7183^(0.065t)
2 = 2.7183^(0.065t)
Taking ln of both sides, it becomes
Ln 2 = 0.065tln2.7183
0.693 = 0.065t
t = 0.693/0.065
t = 10.66
Approximately 17 years
Considering Adam's investment, we would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 480
A = 960
r = 6.75% = 6.75/100 = 0.0675
n = 4 because it was compounded 4 times in a year.
Therefore,.
960 = 480(1 + 0.0675/4)^4 × t
960/480 = (1 + 0.016875)^4t
960/480 = (1.016875)^4t
Taking log of both sides, it becomes
Log 2 = 4t log 1.016875
0.301 = 0.0291t
t = 0.301/0.0291
t = 10.34
Approximately 10 years
