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.