Answer: The amount that Wyatt have in his account than Brianna is
$2420
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 Brianna's investment,
P = 25000
r = 5.125% = 5.125/100 = 0.05125
n = 12 because it was compounded 12 times in a year.
t = 16 years
Therefore,.
A = 25000(1+0.05125/12)^12 × 16
A = 25000(1+0.00427)^192
A = 25000(1.00427)^192
A = 25000 × 2.2662
A = 56655
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.
Considering Wyatt's investment,
P = 25000
r = 5.375% = 5.375/100 = 0.05375
t = 16 years
Therefore,.
A = 25000 x 2.7183^(0.05375 x 16)
A = 25000 x 2.7183^(0.86)
A = 25000 × 2.363
A = 59075
The amount that Wyatt have in his account than Brianna is
59075 - 56655 = $2420
