Could someone help me please?
How much will you have accumulated over a period of 20 years if, in an IRA which has a 10% interest rate compounded monthly, you annually invest:
a)$1
b)$100
c)$20,000
d) Part (a) is called the effective yield for an account. How could part (a) be used to determine parts (b) and parts (c)?
Since you are investing annually, you will need the formula:How much will you have accumulated over a period of 20 years if, in an IRA which has a 10% interest rate compounded monthly, you annually invest:
F is the final value of the investment
P is the initial value of the investment
t is the number of years
A is the amount invested annually
i is the "real" annual interest, given by where k is the number of interest compoundings per year and I is the listed annual interest rate.
Since P=0,
If i and t are considered constants, then F is proportional to A. so if A=100 then F will be
This formula does not apply because the money is being invested annually ie. each year the investor deposits a fixed amount into the account. This is the correct formula for a single initial investment.
With a given nominal rate j compounded m times per year, we define the corresponding effective rate to be that rate w which, if compounded annually, is equivalent to the given rate. That is,
In your particular case, if $1 is invested at the rate 10% compounded 12 times per year, then
Since you’re seeking to calculate the accumulated value of an annual investment over a period of 20 years, you need to make use of the future value formula of an annuity with w = i, n = 20 years, and R = $1, $100, or $20,000.
For the beginning of year deposits/investments, use
For the end of year deposits/investments, use
With a given nominal rate j compounded m times per year, we define the corresponding effective rate to be that rate w which, if compounded annually, is equivalent to the given rate. That is,
In your particular case, if $1 is invested at the rate 10% compounded 12 times per year, then
Since you’re seeking to calculate the accumulated value of an annual investment over a period of 20 years, you need to make use of the future value formula of an annuity with w = i, n = 20 years, and R = $1, $100, or $20,000.
For the beginning of year deposits/investments, use
For the end of year deposits/investments, use