Answer:
$126
Explanation:
We solve using Compound Interest formula
For Matthew
Matthew invested $4,700 in an account paying an interest rate of 3 3/8% compounded monthly.
P = $4700
R = 3 3/8 % = 3.375 %
t = 14 years
n = Compounded Monthly = 12
Hence,
First, convert R as a percent to r as a decimal
r = R/100
r = 3.375/100
r = 0.03375 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 4,700.00(1 + 0.03375/12)^(12)(14)
A = 4,700.00(1 + 0.0028125)^(168)
A = $7,533.80
For Peyton, we are using a different compound interest formula because it is compounded continuously
Peyton invested $4,700 in an account paying an interest rate of 3 1/4%
compounded continuously.
P = $4700
R = 3 1/4 % = 3.25%
t = 14 years
n = Compounded continuously
First, convert R as a percent to r as a decimal
r = R/100
r = 3.25/100
r = 0.0325 rate per year,
Then solve the equation for A
A = Pe^rt
A = 4,700.00e^(0.0325)(14)
A = $7,408.01
After 14 years, the amount of money Matthew would have in his account than Peyton, to the nearest dollar is calculated as:
$7,533.80 - $7,408.01
= $125.79
Approximately = $126 to the nearest dollar