Answer: Madelyn would have $14.17 in her account more than Jonathan.
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 Madelyn's investment,
P = 650
r = 5.75% = 5.75/100 = 0.0575
n = 365 because it was compounded 12 times in a year.
t = 10 years
Therefore,
A = 650(1+0.0575/365)^365 × 10
A = 650(1+0.0001575)^3650
A = 650(1.0001575)^3650
A = 650 × 1.7768
A = 1154.92
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 Jonathan's investment,,
P = 650
r = 5.625% = 5.625/100 = 0.05625
t = 10 years
Therefore,
A = 650 x 2.7183^(0.05625 x 10)
A = 650 x 2.7183^(0.5625)
A = 650 × 1.755
A = $1140.75
The difference in the amount in both accounts is
1154.92 - 1140.75 = $14.17
