Answer: The amount that Sebastian has more than Avery is $1120
Step-by-step explanation:
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
Considering Sebastian's investment,
P = 32000
r = 2.625% = 2.625/100 = 0.02625
n = 12 because it was compounded 12 times in a year.
t = 18 years
Therefore,.
A = 32000(1 + 0.02625/12)^12 × 18
A = 32000(1+0.0021875)^216
A = 32000(1.0021875)^216
A = 32000 × 1.603
A = 51296
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 = 32000
r = 2.5% = 2.5/100 = 0.025
t = 18 years
Therefore,
A = 32000 x 2.7183^(0.025 x 18)
A = 32000 x 2.7183^(0.45)
A = 32000 × 1.568
A = 50176
The amount that Sebastian has more than Avery is
51296 - 50176 = $1120
