Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / Payments of 300, 500 and 700 are made at the end of years five, six, and eight, respectively
Payments of 300, 500 and 700 are made at the end of years five, six, and eight, respectively. Interest is accumulated at an annual effective rate of 4%. You are to find the point in time at which a single payment of $1,500 is equivalent to the above series of payments. You are given: (1)X is the point in time calculated by the method of equated time. (ii) Y is the exact point in time. Calculate X+Y.
1. Point in time : X
Method of equated time (weighted average time) = [∑ (Payments * year) ] / Single Payment
X = [ $300 * 5 + $500 * 6 + $700 * 8 ] / $1500
= 6.733
2. Exact point in time : Y
Exact point of time depends on the interest rate. Here the Annual effective interest rate is 4%. Single payment is $1500.
For the exact point of time single payment present value is equal to all payments present value. So, the following equation is formed :
$1500 * PVIF ( 4% , n ) = $300 * PVIF ( 4% , 5 ) + $500 * PVIF ( 4% , 6 ) + $700 * PVIF ( 4% , 8 ) [ PVIF = Present value interest factor = 1 / (1+r)n , where r = interest rate and n = number of period ]
$1500 * 1 / (1 + 0.04)n = $300 * 0.8219 + $500 * 0.7903 + $700 * 0.7307 [ Values taken directly from PVIF table ]
$1500 / (1 + 0.04)n = $246.57 + $395.15 + $511.49
$1500 / (1 + 0.04)n = $1153.21
1 / (1 + 0.04)n = $1153.21 / $1500
1 / (1 + 0.04)n = 0.7688
n = 6.707 (from working note)
so, Y = 6.707
then X + Y = 6.733 + 6.707 = 13.44
Working Note:
PVIF ( 4%, 6) = 0.7903
PVIF ( 4%, 7) = 0.7599
from unit method; 0.0304 ( 0.7903 - 0.7599 ) decrease when difference is 1 ( 7 - 6 )
0.0215 ( 0.7903 - 0.7688 ) decreases when difference is 0.707 [ ( 1 / 0.0304 ) * 0.0215 ]
so, PVIF ( 4%, 6.707 { 6 + 0.707 } ) = 0.7688
