many people prepare for retirement by making monthly contributions to a savings program. suppose that $2,500…

many people prepare for retirement by making monthly contributions to a savings program. suppose that $2,500 is set aside each year and invested in a savings account that pays 8% interest per year, compounded continuously.\na. determine the accumulated savings in this account at the end of 25 years.\nthe accumulated savings amount at the end of 25 years will be $191,778. (round to the nearest dollar.)\nb. in part (a), suppose that an annuity will be withdrawn from savings that have been accumulated at the eoy 25. the annuity will extend from the eoy 26 to the eoy 32. what is the value of this annuity if the interest and compounding frequency in part (a) do not change?\nthe value of the annuity will be $ . (round to the nearest dollar.)

many people prepare for retirement by making monthly contributions to a savings program. suppose that $2,500 is set aside each year and invested in a savings account that pays 8% interest per year, compounded continuously.\na. determine the accumulated savings in this account at the end of 25 years.\nthe accumulated savings amount at the end of 25 years will be $191,778. (round to the nearest dollar.)\nb. in part (a), suppose that an annuity will be withdrawn from savings that have been accumulated at the eoy 25. the annuity will extend from the eoy 26 to the eoy 32. what is the value of this annuity if the interest and compounding frequency in part (a) do not change?\nthe value of the annuity will be $ . (round to the nearest dollar.)

Answer

Explanation:

Step1: Recall the future - value of an ordinary annuity formula

The formula for the future - value of an ordinary annuity is $F = A\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods. Here, $A=$2500$, $r = 0.08$ (8% annual interest rate), and $n = 25$ years.

Step2: Substitute the values into the formula

$F=2500\times\frac{(1 + 0.08)^{25}-1}{0.08}$. First, calculate $(1 + 0.08)^{25}$. Using the formula $a^{n}=e^{n\ln(a)}$, $(1 + 0.08)^{25}=e^{25\ln(1.08)}\approx6.848477$. Then $(1 + 0.08)^{25}-1\approx5.848477$.

Step3: Calculate the future - value

$F = 2500\times\frac{5.848477}{0.08}=2500\times73.105963\approx182764.91\approx182765$.

Answer:

182765