I need help answering this problem:

A sequence of 8 annual payments of 750 each, with the first payment due at the beginning of the 6th year; money is worth 6%.

(The beginning of year 6 is the end of year 5.) Find the present value.

This is my answer: 750 [ (1-1.06^-13) / .06 ] - 750 [ (1-1.06^-5) / .06 ] = 3,480.24

and this is the book's: 3,689 .

The book didn't provide a solution, so I would really appreciate it if someone can help me find where my solution went

wrong. Thank you!

Present value formula

Code:

PV = R . (1+i*type) . (1+i)^-d [ 1 - (1+i)^-n ] / i

where

R = annuity payment

i = interest rate

type = 0 for end of period payments, 1 for start of period payments

d = time period by which annuity is deferred

n = total number of payments

Your problem has the following data

Code:

PV = R . (1+i*type) . (1+i)^-d [ 1 - (1+i)^-n ] / i
R = 750
i = 6% = 0.06
type = 1 for start of period annuity
d = 5 as the first payment is deferred by 5 periods
n = 8 as there are 8 annuity payments
750 (1+6%)^-5 (1+6%) [ 1-(1+6%)^-8 ] / 6%
750 (1+0.06)^-5 (1+0.06) [ 1-(1+0.06)^-8 ] / 0.06
750 (1.06)^-5 (1.06) [ 1-(1.06)^-8 ] / 0.06
750 (0.74725817286605716719189988974845) (1.06) [ 1-0.62741237134182678250493686881491 ] / 0.06
750 (0.74725817286605716719189988974845) (1.06) [ 0.37258762865817321749506313118509 ] / 0.06
750 (0.74725817286605716719189988974845) (1.06) (6.2097938109695536249177188530833)
750 (0.74725817286605716719189988974845) (6.5823814396277268424127819842683)
750 (4.9187383276836621437572364513326)
PV = 3689.05