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:

Amira deposits $560 every quarter into an account earning an annual interest rate of 8% compounded quarterly. How much would she have in the account after 12 years, 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:

Amira deposits $560 \$ 560 every quarter into an account earning an annual interest rate of 8% 8 \% compounded quarterly. How much would she have in the account after 1212 years, 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. Amira deposits $560 \$ 560 every quarter into an account earning an annual interest rate of 8% 8 \% compounded quarterly. How much would she have in the account after 1212 years, 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.\newlineAmira deposits $560\$560 every quarter, so d=$560d = \$560.\newlineThe annual interest rate is 8%8\%, so the quarterly interest rate i=8%4=2%i = \frac{8\%}{4} = 2\% per quarter.\newlineSince the interest is compounded quarterly, we need to find the number of quarters in 1212 years. There are 44 quarters in a year, so n=12 years×4 quarters/year=48n = 12 \text{ years} \times 4 \text{ quarters/year} = 48 quarters.
  2. Convert Interest Rate: Convert the quarterly interest rate into decimal form. i=2%i = 2\% per quarter =2100=0.02= \frac{2}{100} = 0.02
  3. Calculate (1+i)n(1+i)^n: Use the formula A=d((1+i)n−1i)A = d\left(\frac{(1+i)^{n}-1}{i}\right) to calculate the future value of the account.\newlineFirst, calculate (1+i)n(1+i)^n.\newline(1+i)n=(1+0.02)48(1+i)^n = (1+0.02)^{48}
  4. Calculate (1+0.02)48(1+0.02)^{48}: Calculate (1+0.02)48(1+0.02)^{48} using a calculator.\newline(1+0.02)48≈2.20804(1+0.02)^{48} \approx 2.20804
  5. Calculate Numerator: Calculate the numerator of the formula: ((1+i)n−1)((1+i)^{n}-1). ((1+0.02)48−1)≈(2.20804−1)≈1.20804((1+0.02)^{48} - 1) \approx (2.20804 - 1) \approx 1.20804
  6. Calculate Future Value: Calculate the future value AA using the formula.A=560×(1.208040.02)A = 560 \times \left(\frac{1.20804}{0.02}\right)
  7. Division and Multiplication: Calculate the division and multiplication to find AA.A≈560×(60.402)≈33825.12A \approx 560 \times (60.402) \approx 33825.12
  8. Round Future Value: Round the future value to the nearest dollar. \newlineA≈$33,825A \approx \$33,825

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