Brianna invested $990 in an account paying an interest rate of 9 3 4 9 4 3 % compounded continuously. Penelope invested $990 in an account paying an interest rate of 9 1 2 9 2 1 % compounded monthly. After 16 years, how much more money would Brianna have in her account than Penelope, to the nearest dollar?

Brianna would have $177 more in her account than Penelope after 16 years.

Step-by-step explanation:

Note: There are errors in the question especially in how the interest rates are stated. These are therefore fixed before answering the question. The complete question with the fixed errors is given as follows:

Brianna invested $990 in an account paying an interest rate of 9.34943% compounded continuously. Penelope invested $990 in an account paying an interest rate of 9.12921% compounded monthly. After 16 years, how much more money would Brianna have in her account than Penelope, to the nearest dollar?

The explanation to the answers is now provided as follows:

Step 1: Calculation of the amount of money Brianna would have in her account after 16 years

Since the interest rate is compounded continuously, the amount can be calculated using the formula for calculating the future of value (FV) with a continuous compounding interest rate as follows:

FVB = Pe^(rt) …………………………. (1)

Where;

FVB = Future value or the amount of money Brianna would have in her account after 16 years = ?

P = Amount invested = $990

e = exponential function

r = interest rate = 9.34943%, or 0.0934943

t = number of years = 16

Substituting the values into equation (1), we have:

FVB = $990 * e^(0.0934943 * 16)

FVB = $990 * e^(1.4959088)

FVB = $990 * 4.46339103998695

FVB = $4,418.75712958708

Rounding to the nearest dollar, we have:

FVB = $4,419

Therefore, Brianna would have $4,419 in her account after 16 years.

Step 2: Calculation of the amount of money Penelope would have in her account after 16 years

Since the interest rate is compounded monthly, the amount is calculated using the normal formula for calculating the future value as follows:

FVP = P * (1 + R)^n …………………………. (2)

Where;

FVP = Future value or the amount of money Penelope would have in her account after 16 years = ?

P = Amount invested = $990

R = monthly interest rate = Interest rate / 12 months = 9.12921% / 12 = 0.0912921 / 12 = 0.007607675

t = number of months = number of years * 12 months = 16 * 12 = 192

Substituting the values into equation (2), we have:

FVP = $990 * (1 + 0.007607675)^192

FVP = $990 * 1.007607675^192

FVP = $990 * 4.28510670976906

FVP = $4,242.25564267137

Rounding to the nearest dollar, we have:

FVP = $4,242

Therefore, Penelope would have $4,242 in her account after 16 years.

Step 3: Calculation of the amount of money Brianna would have more in her account than Penelope after 16 years

From Step 1 above, we have:

FVB = Future value or the amount of money Brianna would have in her account after 16 years = $4,419

From Step 2 above, we have:

FVP = Future value or the amount of money Penelope would have in her account after 16 years = $2,242

The amount of money Brianna would have more in her account than Penelope after 16 years can be calculated by deducting FVP from FVB to obtain the difference as follows:

Difference = FVB - FVP = $4,419 - $4,242 = $177

Therefore, Brianna would have $177 more in her account than Penelope after 16 years.

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5/12, or 5: 12

step-by-step explanation: