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!
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
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.
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
To calculate the number of payments for an annuity, we can use the present value formula.
In this case, the present value of the annuity due is $5600, and it is payable semi-annually. The annuity is computed at an interest rate of 6%, compounded semi-annually.
The formula to calculate present value of an annuity due is:
PV = P * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
P = Payment amount
r = Interest rate per period
n = Number of periods
To find the number of payments (n), we need to rearrange the formula to solve for n:
n = - log(1 - (PV * r) / P) / log(1 + r)
Now we can substitute the given values into the formula:
PV = $5600
P = $400 (payment amount)
r = 0.06 (6% as a decimal)
By plugging in these values, we can calculate the number of periods (n).