Question

Madelyn invested $650 in an account paying an interest rate of 5 3/4 % compounded daily. Jonathan invested $650 in an account paying an interest rate of 5 5/8% compounded continuously. After 10 years, how much more money would Madelyn have in her account than Jonathan, to the nearest dollar?

Answer 1

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