# Math

How much money must be deposited now at 6% interest compounded semiannually to yield an annuity payment of \$4,000 at the beginning of each six-month period for a total of five years answer needs to be rounded to the nearest cent

I got \$29,440.36

choices are \$38,120.80 or \$35,144.44
(and the one I picked)

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1. I used
PV = paym[1 - (1+i)^-n]/i

= 4000(1 - 1.03^-10)/.03
= 34120.81 which is none of the answers, but I am 99.9% sure of my answer.

This assumes that the first withdrawal would be 6 months from now.
It would be rather silly to deposit a large sum and immediately make a withdrawal.

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2. How much money must be deposited now at 6% interest compounded semiannually to yield an annuity payment of \$4,000 at the beginning of each six-month period for a total of five years answer needs to be rounded to the nearest cent

I got \$29,440.36

choices are \$38,120.80 or \$35,144.44
(and the one I picked)

The present value of an ordinary annuity is the sum of the present value of the future periodic payments at the point in time one period before the first payment.

What is the amount that must be paid (Present Value) for an annuity with a periodic payment of R dollars to be made at the end of each year for N years, at an interest rate of I% compounded annually? For this scenario,

P = R[1 - (1 + i)^(-n)]/i

where P = the Present Value, R = the periodic payment, n = the number of payment periods, and i = I/100.

Example: What is the present value of an annuity that must pay out \$12,000 per year for 20 years with an annual interest rate of 6%? Here, R = 12,000, n = 20, and i = .06 resulting in

P = 12000[1 - (1.06)^-20]/.06 = \$137,639

P = R[1 - (1 + i)^(-n)]/i

P = 4000[1 - (1.06)^(-10)]/.03 = 34,121.

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