Barb and John Reed want to know how much they must deposit in a retirement savings account today to have payments of $1750 every six months for 15 years. The retirement account is paying 8% annual interest, compounded semiannually?

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Oddman answered
In order to receive 30 payments of $1750, the couple must have $30,261.06 on deposit at the beginning of the period. The first payment will come at the end of the first 6 month period.
You can use this calculator to arrive at the above result. To do so, you need to recognize that it calculates in terms of monthly payments and annual interest rates. That is, the rate applicable to a payment interval is 1/12 of the rate you fill into the form. For your problem, you need to tell it 2.5 years (30 payments) and a rate of 48 (corresponding to 4% per payment interval).

The formula for the amount is the formula for an ordinary annuity   a = pmt (1 - (1 + I)^-n)/I
where pmt = $1750, I = .04, n = 30.

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