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Suppose we deposit $2519 in a savings account earning 2.5% per year, compounded annually. Calculate the value of the account at the end of year 34. Do not round until the very last calculation. Then round your answer to the nearest whole number.

User ManuelMB
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1 Answer

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Final answer:

Using the compound interest formula A = P(1 + r/n)^(nt), with a principal of $2519, an annual rate of 2.5%, compounded annually over 34 years, the account value is approximately $5,155 when rounded to the nearest whole number.

Step-by-step explanation:

To calculate the value of the account at the end of year 34, we can use the compound interest formula, which is:

A = P(1 + r/n)^(nt)

Where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested or borrowed for, in years.

For this problem:

  • P = $2519
  • r = 2.5% or 0.025
  • n = 1 (since the interest is compounded annually)
  • t = 34 years

Now, replace the values in the formula:

A = 2519(1 + 0.025/1)^(1×34)

A = 2519(1 + 0.025)^34

A = 2519(1.025)^34

Calculating this value gives us the future value of the account after 34 years. When you perform the calculation and round to the nearest whole number, you should get:

A ≈ $5,155

Thus, the value of the account at the end of year 34, rounded to the nearest whole number, will be approximately $5,155.

User Ashwin Ramaswami
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