Posted by **Jill** on Tuesday, June 15, 2010 at 3:08pm.

The present value of an annuity due of $400 payable semi-annually is $5600. Interest is computed at 6% compounded semi-annually. what are the number of payments? What formula should I use for this? Thanks!

- Math -
**Reiny**, Tuesday, June 15, 2010 at 5:36pm
sub into your Present Value formula

PV = paym( 1 - (1+i)^-n)/i

5600 = 400 (1 - 1.03^-n)/.03

.42 = 1 - 1.03^-n

1.03^-n = .58

take log of both sides

log(1.03^-n) = log .58

-n(log 1.03) = log .58

-n = log .58/log 1.03

you do the button-pushing, I got 18.4 payments

There will be 18 full payments of $400 plus a partial payment

- Math -
**Jill**, Tuesday, June 15, 2010 at 6:59pm
Thanks so much. That was my answer but that formula in my book was for ordinary annuities and I wasn't sure if it applied to annuities DUE also.

- correction - maths -
**Reiny**, Tuesday, June 15, 2010 at 7:41pm
I did not catch the "due" part

so I would change it to

5600 = 400 + 400 (1 - 1.03^-n)/.03 , one 400 plus n payments

5200 = 400 (1 - 1.03^-n)/.03

.39 = 1 - 1.03^-n

1.03^-n = .61

.

-n = log .61/log 1.03

-n = -16.722

n = 16.7

So in addition to the first 400 payment we need 16 more full payments, plus a partial payment

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