Question

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!

Answer 1

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

Answer 2

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.

Answer 3

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