🎁BACK-TO-SCHOOL DEAL. Subscribe Now to get 40% OFF at only 8.49 USD/month, only valid until Sep 30th, 2024

Question

What is the accumulated sum of the following stream of payments?$2,587 every year at the end of the year for 15 years at 7.50 percent, compounded annually.

Asked By CelestialDreamer51 at

Answered By Expert

Earl

Expert · 3.7k answers · 3k people helped

Sign in to see the answer

Solution By Steps

Step 1: Identify the formula for the accumulated sum of an annuity

The formula to calculate the future value of an annuity is:

FV = P imes \left( \frac{(1 + r)^n - 1}{r} \right)

where

P is the periodic payment,

r is the interest rate per period, and

n is the number of periods.

Step 2: Substitute the given values into the formula

Given:

P = 2587

r = 0.075

n = 15

Substitute these values into the formula:

FV = 2587 imes \left( \frac{(1 + 0.075)^{15} - 1}{0.075} \right)

Step 3: Calculate the compound factor

Calculate

(1 + 0.075)^{15}:

(1.075)^{15} \approx 2.961

Step 4: Calculate the numerator of the fraction

2.961 - 1 = 1.961

Step 5: Divide by the interest rate

\frac{1.961}{0.075} \approx 26.147

Step 6: Multiply by the periodic payment

2587 imes 26.147 \approx 67632.289

Final Answer

The accumulated sum of the stream of payments is approximately $67,632.29.

🧑‍🏫 More Questions

Which laboratory activity involves a chemical change? leaving a copper penny in vinegar until it turns greenboiling saltwater for several minutes until only solid salt remainsextracting iron filings from a sand mixture using a magnetcrushing a rock with a hammer to extract mineral deposits

write a story about a green dancing Octopus. Set the story in Sam Bankman-Fried's FTX offices on November 8, 2022 in 5 or 7 sentences

Promp Can I get the Crimson Deathcharger mount on a priest in Wrath classic? A Yes, a priest can obtain this mount. Aryone can obtain the Crimuon Deathcharger mount in the World of Warcraft Wrath of the Lich King Clasic game. The mount is obtained by completing the quest for the legendary swoed Shadowmournt. Upon completion of this complex quest chain, the priest will receive a set of rewards which includes the Reins of the Crimson Deathcharger, a tabard, a locket, a munic box, and the Muradin's Favor item. B Yes, a priest can obtain the Crimson Deathcharger mount. The Crimson Deathcharger mount in the World of Warcraft Wrath of the Lich King Classic game is a reward for the completion of the Shadowmourne quest chain. Shadowmourne is a legendary quality weapon in the game, and the quest to obtain it is complex, involving many steps. In addition to the Shadowmourne weapon, there are five special rewards for completion of the quest chain, and the Crimson Deathcharger mount is among these rewands. The quest chain is not avalable to atf players, but the additional rewards (including the Crimson Deathcharger mount) can be traded or sold to other players.

Which term best describes a mathematical statement of the form shown below? If $A$, then $B$. A. Proof B. Conditional statement C. Deductive statement D. Conjecture

What is $\frac{4}{15}$ written as a recurring decimal using dot notation?