Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Sophia is saving money and plans on making monthly contributions into an account earning an annual interest rate of 6.3% compounded monthly. If Sophia would like to end up with $65,000 after 11 years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer. A=d(((1+i)^(n)-1)/(i)) A= the future value of the account after n periods d= the amount invested at the end of each period i= the interest rate per period n= the number of periods Answer:

Sophia is saving money and plans on making monthly contributions into an account earning an annual interest rate of 6.3% 6.3 \% compounded monthly. If Sophia would like to end up with $65,000 \$ 65,000 after 1111 years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n−1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Compound interestright chevron icon

Full solution

Q. Sophia is saving money and plans on making monthly contributions into an account earning an annual interest rate of 6.3% 6.3 \% compounded monthly. If Sophia would like to end up with $65,000 \$ 65,000 after 1111 years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.\newlineA=d((1+i)n−1i) A=d\left(\frac{(1+i)^{n}-1}{i}\right) \newlineA= A= the future value of the account after n n periods\newlined= d= the amount invested at the end of each period\newlinei= i= the interest rate per period\newlinen= n= the number of periods\newlineAnswer:
  1. Identify Given Values: Identify the given values from the problem.\newlineAA (future value of the account) = $65,000\$65,000\newlineii (monthly interest rate) = 6.3%6.3\% annual interest rate / 1212 months = 0.063/120.063 / 12\newlinenn (total number of periods) = 1111 years * 1212 months/year
  2. Convert Annual Interest Rate: Convert the annual interest rate to a monthly interest rate. \newlinei=0.06312i = \frac{0.063}{12}\newlinei=0.00525i = 0.00525 (monthly interest rate)
  3. Calculate Total Periods: Calculate the total number of periods (months) over 1111 years.\newlinen=11 years×12 months/yearn = 11 \text{ years} \times 12 \text{ months/year}\newlinen=132 monthsn = 132 \text{ months}
  4. Find Monthly Contribution: Use the formula to find the monthly contribution dd.A=d×((1+i)n−1i)A = d \times \left(\frac{(1 + i)^{n} - 1}{i}\right)$65,000=d×((1+0.00525)132−10.00525)\$65,000 = d \times \left(\frac{(1 + 0.00525)^{132} - 1}{0.00525}\right)
  5. Calculate Value Inside Parentheses: Calculate the value inside the parentheses and the exponent.\newline(1+0.00525)132−1(1 + 0.00525)^{132} - 1
  6. Perform Exponentiation: Perform the exponentiation.\newline(1+0.00525)132≈1.99624(1 + 0.00525)^{132} \approx 1.99624\newline1.99624−1≈0.996241.99624 - 1 \approx 0.99624
  7. Divide by Monthly Interest Rate: Divide the result by the monthly interest rate.\newline0.99624/0.00525≈189.736190.99624 / 0.00525 \approx 189.73619
  8. Solve for 'd': Solve for 'd' by dividing the future value of the account by the result from the previous step.\newline$65,000/189.73619≈$342.58\$65,000 / 189.73619 \approx \$342.58
  9. Round Monthly Contribution: Round the monthly contribution to the nearest dollar. \newlined≈$343d \approx \$343 per month

More problems from Compound interest

Question
Johnny bought an oil painting originally priced at $80 but on sale for 5050% off. After 1010% sales tax, what was the total cost?\newline`$`____
Get tutor helpright-arrow

Posted 4 months ago

Question
It costs `$40` to buy 44 ironing boards. If the ironing boards all have the same price, how much does it cost to buy 11 ironing board? ` $`_____
Get tutor helpright-arrow

Posted 7 months ago

Question
Whitney buys a lamp online for $93\$93. If shipping and handling are an additional 10%10\% of the price, how much shipping and handling will Whitney pay? \newline $\$ _____\_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
A 99-foot roll of plastic wrap costs $5.40\$5.40. What is the price per inch? \newline $\$ _____
Get tutor helpright-arrow

Posted 7 months ago

Question
A store purchased canoes for $300\$300 and sold them for $435\$435. What percentage is the mark-up? \newlineWrite your answer using a percent sign (%\%). \newline _____
Get tutor helpright-arrow

Posted 7 months ago

Question
A ceramic vase was originally priced at $100\$100 but went on sale for 50%50\% off. If Ernesto bought the ceramic vase and paid 12%12\% sales tax, how much did he pay in total? \newline $\$ ____
Get tutor helpright-arrow

Posted 7 months ago

Question
A 1212-foot roll of aluminum foil costs $7.20\$7.20. What is the price per inch?
Get tutor helpright-arrow

Posted 9 months ago

Question
A 1515-foot roll of paper towel costs $9.75\$9.75. What is the price per inch?
Get tutor helpright-arrow

Posted 7 months ago

Question
A 2020-foot roll of ribbon costs $8.00\$8.00. What is the price per inch?
Get tutor helpright-arrow

Posted 9 months ago

Question
A 66-foot roll of fabric costs $4.50\$4.50. What is the price per inch? \newline $\$ ______
Get tutor helpright-arrow

Posted 7 months ago

View all (77)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant