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Brianna invested $25,000 in an account paying an interest rate of 5 1/8% compounded monthly. Wyatt invested $25,000 in an account paying an interest rate of 5 3/8% compounded continuously. After 16 years, how much more money would Wyatt have in his account than Brianna, to the nearest dollar?

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

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