Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Recently, More Money 4U offered an annuity that pays 5.1% compounded monthly. If $1,718 is deposited into this annuity every​ month, how much is in the account after 8 ​years? How much of this is​ interest?

Sagot :

semsee45

Answer:

Account balance = $203,131.31

Interest = $38,203.31

Step-by-step explanation:

To determine how much is in the account after 8 years, we can use the Future Value of Annuity formula:

[tex]FV=\dfrac{PMT\left[\left(1+\dfrac{r}{n}\right)^{nt}-1\right]}{\dfrac{r}{n}}[/tex]

where:

  • FV = Future value
  • PMT = Regular deposit amount
  • r = Annual interest rate (decimal form)
  • n = number of times interest is compounded per year
  • t = time in years

In this case:

  • PMT = $1,718
  • r = 5.1% = 0.051
  • n = 12 (monthly)
  • t = 8 years

Substitute the values into the formula and solve for FV:

[tex]FV=\dfrac{1718\left[\left(1+\dfrac{0.051}{12}\right)^{12 \cdot 8}-1\right]}{\dfrac{0.051}{12}}[/tex]

[tex]FV=\dfrac{1718\left[\left(1.00425\right)^{96}-1\right]}{0.00425}[/tex]

[tex]FV=\$203131.31[/tex]

Therefore, the future value of the annuity after 8 years is $203,131.31.

To calculate how much of the balance is interest, subtract the monthly payment (PMT) multiplied by the number of payments (nt) from the future value (FV):

[tex]\textsf{Interest}=FV-PMT \cdot nt \\\\ \textsf{Interest}=203131.31-1718\cdot 12 \cdot 8 \\\\ \textsf{Interest}=203131.31-164928 \\\\ \textsf{Interest}=\$38203.31[/tex]

Therefore, the interest earned over the 8 years is $38,203.31.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.