213k views
4 votes
Matthew invested $4,700 in an account paying an interest rate of 3 3/8% compounded

monthly. Peyton invested $4,700 in an account paying an interest rate of 3 1/4%
compounded continuously. After 14 years, how much more money would Matthew
have in his account than Peyton, to the nearest dollar?

2 Answers

3 votes

Answer:

126

Explanation:

126 to the nearest dollar

User Jason Wiener
by
8.2k points
4 votes

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

User Jeremy Savage
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories