Question

Bilquis invested $6,900 in an account paying an interest rate of 5(1/8)% compounded continuously. Sophie invested $6,900 in an account paying an interest rate of 4(3/4)% compounded monthly. After 18 years, how much more money would Bilquis have in her account than Sophie, to the nearest dollar?

Answer 1

To calculate the total amount of money in an account after a given number of years with continuous compounding, we use the formula
`A = P * e^{(rt)`. Bilquis would have $3,565.39 more in her account than Sophie after 18 years.

Step-by-step explanation:

To calculate the total amount of money in an account after a given number of years with continuous compounding, we use the formula
`A = P * e^{(rt)`, where A is the future amount, P is the principal, e is the base of the natural logarithm, r is the interest rate, and t is the time in years.

For Bilquis, P = $6,900, r = 5 (1/8)% = 0.05125, and t = 18. Plugging in these values, we get
`A = $6,900 * e^((0.05125*18)) = $20,092.97` (rounded to the nearest dollar).

For Sophie, P = $6,900, r = 4 (3/4)% = 0.0475, and t = 18. Plugging in these values, we get
`A = $6900 * (1 + 0.0475/12)^((12*18)) = $16,527.58` (rounded to the nearest dollar).

The difference between Bilquis and Sophie's accounts after 18 years is $20,092.97 - $16,527.58 = $3565.39 (rounded to the nearest dollar).

Answer 2

Bilquis would have approximately $3,097.38 more in her account than Sophie after 18 years.

For Bilquis, her initial investment is $6,900, and the interest rate is 5(1/8)% or 5.125% compounded continuously. The formula to calculate the future value with continuous compounding is:

A = P * e^(rt)

Where:

A = future value

P = principal (initial investment)

e = mathematical constant approximately equal to 2.71828

r = interest rate as a decimal

t = time in years

Plugging in the values, we get:

A = 6900 * e^(0.05125 * 18)

For Sophie, her initial investment is also $6,900, and the interest rate is 4(3/4)% or 4.75% compounded monthly. The formula to calculate the future value with monthly compounding is:

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

Where:

A = future value

P = principal (initial investment)

r = interest rate as a decimal

n = number of times interest is compounded per year

t = time in years

Plugging in the values, we get:

A = 6900 * (1 + 0.0475/12)^(12 * 18)

Now we can calculate the future values for both Bilquis and Sophie's investments using the respective formulas.

Calculating the future value for Bilquis' investment, we get:

A = 6900 * e^(0.05125 * 18) = approximately $18,641.86

Calculating the future value for Sophie's investment, we get:

A = 6900 * (1 + 0.0475/12)^(12 * 18) = approximately $15,544.48

Now, to find the difference, we subtract Sophie's future value from Bilquis' future value:

$18,641.86 - $15,544.48 = approximately $3,097.38