Kaylee invested $860 in an account paying an interest rate of 6 1/8% compounded annually. Gabriel invested $860 in an account paying an interest rate of 6 1/2% compounded continuously. To the nearest dollar, how much money would Kaylee have in her account when Gabriel's money has tripled in value?

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Kaylee invested $860 in an account paying an interest rate of 6 1/8% compounded annually. Gabriel invested $860 in an account paying an interest rate of 6 1/2% compounded continuously. To the nearest dollar, how much money would Kaylee have in her account when Gabriel's money has tripled in value?

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fichoh fichoh · Answer 1 · 2025-03-31T02:17:47-04:00

Answer:

$2415

Step-by-step explanation:

Compound interest :

A = P(1 + r/n)^nt

n = number of compounding times per period

A = final amount ; P = initial investment

For account compounded continuously :

A = Pe^it

i = interest ; t number of years ;

Gabriel:

P = $860 ; i = 6 1/2 % = 13/2% = 0.065

When P triples ; A = 860 * 3 = 2580

2580 = 860*e^0.065t

2580/860 = e^0.065t

3 = e^0.065t

Take In

In(3) = 0.065t

1.0986122 = 0.065t

t = 1.0986122 / 0.065

t = 16.90 years

Kaylee's account at t = 16.90 years

Number of months = 16. 9 * 12 = 202.8 = 203

Rate = 6 1/8% = 6.125% = 0.06125

A = 860(1 + 0.06125 / 12)^202.8

A = 860(1 + 0.0051041) ^202.8

A = 860(1.0051041)^202.8

A = 860 * 2.8080176

A = 2414.8951

A = $2415