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:

You can retry this question below How much should be invested now at 3.1% compounded semiannually to have $40,000 in 19 years?

You can retry this question below\newlineHow much should be invested now at 3.1% 3.1 \% compounded semiannually to have $40,000 \$ 40,000 in 1919 years?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Finance problemsright chevron icon

Full solution

Q. You can retry this question below\newlineHow much should be invested now at 3.1% 3.1 \% compounded semiannually to have $40,000 \$ 40,000 in 1919 years?
  1. Identify variables: Identify the variables from the problem.\newlineWe have:\newlineFuture Value (FV) = $40,000\$40,000\newlineAnnual interest rate (r) = 3.1%3.1\% or 0.0310.031\newlineNumber of times the interest is compounded per year (n) = 22 (since it's compounded semiannually)\newlineNumber of years (t) = 1919\newlineWe need to find the Present Value (PV), which is the initial investment amount.
  2. Convert interest rate: Convert the annual interest rate to the rate per compounding period.\newlineSince the interest is compounded semiannually, we divide the annual rate by the number of compounding periods per year.\newlineRate per period r/nr/n = 0.031/2=0.01550.031 / 2 = 0.0155
  3. Calculate compounding periods: Calculate the total number of compounding periods.\newlineTotal number of compounding periods ntnt = n×tn \times t = 2×192 \times 19 = 3838
  4. Use present value formula: Use the formula for the present value of an investment compounded semiannually to find the initial investment amount.\newlineThe formula is:\newlinePV=FV(1+rn)ntPV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
  5. Calculate present value: Plug the values into the formula and calculate the present value.\newlinePV = $40,000/(1+0.0155)38\$40,000 / (1 + 0.0155)^{38}\newlinePV = $40,000/(1.0155)38\$40,000 / (1.0155)^{38}\newlinePV = $40,000/(1.015538)\$40,000 / (1.0155^{38})\newlinePV = $40,000/(1.933384...)\$40,000 / (1.933384...)\newlinePV ≈ $40,000/1.933384\$40,000 / 1.933384\newlinePV ≈ $20,684.03\$20,684.03

More problems from Finance problems

Question
Solve. Write your answer as an integer or a fraction in simplest form.\newline5x=15^x=1\newlinex=x= _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Steven opened a savings account and deposited $100.00\$100.00 as principal. The account earns 9%9\% interest, compounded annually. What is the balance after 55 years?\newlineUse the formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where AA is the balance (final amount), PP is the principal (starting amount), rr is the interest rate expressed as a decimal, nn is the number of times per year that the interest is compounded, and tt is the time in years.\newlineRound your answer to the nearest cent.\newline$\$____
Get tutor helpright-arrow

Posted 2 months ago

Question
Use the following function rule to find f(1) f(1) .\newlinef(x)=12(7)x+8 f(x) = 12(7)^x + 8 \newlinef(1)= f(1) = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
The town of Valley View conducted a census this year, which showed that it has a population of 1,8001,800 people. Based on the census data, it is estimated that the population of Valley View will grow by 12%12\% each decade.\newlineWrite an exponential equation in the form y=a(b)xy = a(b)^x that can model the town population, yy, xx decades after this census was taken.\newlineUse whole numbers, decimals, or simplified fractions for the values of aa and bb.\newliney=y = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve. Round your answer to the nearest thousandth.\newline7=9x7 = 9^x\newlinex=x = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve. Round your answer to the nearest thousandth.\newline7=ex7 = e^x\newlinex=x = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve. Simplify your answer.\newlinelog⁡u=1\log u = 1\newlineu=u = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve. Simplify your answer.\newline7log⁡x=77\log x = 7\newlinex=x = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
How does g(t)=3t g(t) = 3^t change over the interval from t=3 t = 3 to t=4 t = 4 ?\newlineChoices:\newline(A) g(t) g(t) decreases by 3 3 \newline(B) g(t) g(t) increases by 3 3 \newline(C) g(t) g(t) decreases by 3% 3\%\newline(D) g(t) g(t) increases by 200%200\%
Get tutor helpright-arrow

Posted 2 months ago

Question
A function f(x) f(x) increases by 6 6 over every unit interval in x x and f(0)=0 f(0) = 0 .\newlineWhich could be a function rule for f(x) f(x) ?\newlineChoices:\newline(A) f(x)=6xf(x) = 6^x\newline(B) f(x)=6xf(x) = 6x\newline(C) f(x)=16xf(x) = \frac{1}{6^x}\newline(D) f(x)=x6f(x) = \frac{x}{6}
Get tutor helpright-arrow

Posted 2 months ago

View all (53)