X??

p= m/(1+rt) ...........this is the formula given

2000= X/(1+0.15*6/12) + X/(1+0.15*12/12) ....the interest is applied per year. we have 2 payments, one is after 6 months, the other is after a year. 6 months is 6/12 of a year (since we have 6 out of 12 months--so it's half a year), so we plug in 6/12 for t in the first part. 12/12 means 12 months out of 12 months, which is just one, so that's when the interest is applied after one year, so we put that for t in the second part of the formula. 15% = 0.15 as i explained earlier, so that is what we plug in for r in both parts of the formula. and now we just need to solve for x

we get,

2000 = x/1.075 + x/1.15 ........adding these fractions we get

2000 = 1.799797776x

=> x = 2000/1.799797776 = 1111.24

M= p(1+rt)Quote:

if the datum date was changed to be 1/6/2001.calculate the value of each payment.

M= 2000 (1+0.15*1)= 2300

So, 2300 = X (1 + 0.15 * 6/12) + X

2300=2.075 X

X= 1108.43

.....here we just applied the formula with p = 2000, t = 1 since it's after 1 year, r = 0.15 = 15% and solved for x

for the first: x/1.075 + x/1.15 = x(1/1.075 + 1/1.15) if we factor out the x

so we just add the numbers in the brackets to get the coefficient of x, and then we divide both sides by that number to get x by itself on one side of the equation