Respuesta :
Answer:
Option d)$401,447.24
Step-by-step explanation:
We are given that as part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each year at rate of 6% compounded annually for 20 years
So first of all we need to find the future value of annuity using the formula as shown below :
[tex]FV= p\frac{[(1+\frac{r}{n})^{(n)(t)}-1)]}{\frac{r}{n}}[/tex]
Here, FV = future value of annuity
p = $35000 (annual deposit)
r is rate = 6% = 0.06
n = number of compounding = 1 ( as we are compounding annually )
t = number of years = 20
So plugging in all the values in the formula , we get
[tex]FV= 35000\frac{[(1+\frac{0.06}{1})^{(1)(20)}-1)]}{\frac{0.06}{1}}[/tex]
Simplifying further , we get
[tex]FV= 35000\frac{[(1+0.06)^{20}-1)]}{0.06}[/tex]
Plugging in the given values in the calculator , we get
FV = $ 1287495.69
So far we have got the Total amount for annuity , from here we need to use the concept of compound interest and find the principal amount to be deposited to get the required total amount of $ 1287495.69
The formula for compound interest when compounded annually is given by:
[tex]A=P(1+r)^t[/tex]
Here A = 1287495.69 (Total amount required)
P = ( principal amount to be deposited to meet the required total amount )
r = 6% = 0.06
t = 20
So plugging in all the known values in the formula , we get
[tex]1287495.69= P(1+0.06)^{20}[/tex]
simplifying further, we get
[tex]\frac{1287495.69}{(1.06)^{20}}= P[/tex]
so required amount to be deposited is given by :
P = $401,447.24
Hope it was helpful !:)
