How much will you have accumulated over a period of 30 years if, in an IRA which has a 10% interest rate compounded quarterly, you annually invest:
a. $1
b. $4000
c. $10,000
d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine
Parts (b) and (c)? (Your answer should be in complete sentences free of grammar, spelling,
and punctuation mistakes.)
Thank you for the help!!
a) amount = 1(1.10^30 - 1)/.10
I just used the basic annuity formula
b) amount = 4000(1.10^30 - 1)/.10
So once you have a), the amount that $1 produces, you simply have to multiply that
by the different investment values.
let me know what you get for c).
To determine how much you will have accumulated over a period of 30 years with different annual investments in an IRA with a 10% interest rate compounded quarterly, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = the accumulated amount
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
a. For an annual investment of $1:
P = 1, r = 0.10, n = 4 (quarterly compounded), and t = 30 (years).
Using the formula: A = 1 * (1 + 0.10/4)^(4*30), we can calculate the accumulated amount.
b. For an annual investment of $4000:
The effective yield from part (a) can be multiplied by $4000 to calculate the accumulated amount.
c. For an annual investment of $10,000:
Using the same concept, the effective yield from part (a) can be multiplied by $10,000 to calculate the accumulated amount.
d. Part (a) can be used to determine parts (b) and (c) by calculating the effective yield. The effective yield is the accumulated amount for a $1 investment. By applying this effective yield to the larger investments in parts (b) and (c), we can determine how much would be accumulated over 30 years.
It is important to note that the formula assumes no additional contributions or withdrawals during the 30-year period and that the interest rate remains constant.