A 45 year old man deposits a total of dollar 2000 per year in an IRA at the end of each year until age 65.how much money will be in the account if the interest rate is 10%compounded semiannual with payments made at the end of each semiannual period
Since the payment period and the interest period do not coincide, our normal formula cannot be used.
So we have to change the 10% per annum compounded semiannually to an
equivalent annual rate.
let that rate be i, so then
(1 + i)^1 = 1.05^2
1+i = 1.1025
i = .1025
n = 20
paym = 2000
amount = 2000(1.1025^20 - 1)/.1025
= 117,853.44
At the end of you problem you state "10%compounded semiannual with payments made at the end of each semiannual period" but
you don't say what that payment is.
To assume 2 payments of 1000 at the end of each half year is the same as
a single payment of 2000 is totally invalid, but I think somehow that is what the author wants you to do. It would be true only if the interest rate is 0%.
So this is a poorly worded question.