# Compound interest at changing interest rates

• Oct 20th 2010, 07:26 PM
teerplid
Compound interest at changing interest rates
A young couple owns a block of land worth \$29000. They are offered 20% deposit and 2 equal payments of \$15000 at the end of years 2 and 4. If money is worth J2=8% for the first 2 years and J4=12% for the next 2 years, should they accept the offer?

I tried [2*(15000)*(1.04^-4)(1.03^-8)]+(29000*.2) answer comes out to 26043.71 so they should not accept, but i think ive skipped some things and done something wrong, the answer in the back says they shouldnt accept but i think i still messed up somehow. Any help is appreciated :) thanks, teerplid.
• Oct 21st 2010, 03:56 AM
dexteronline
PV = \$29,000x20% + \$15,000(1+8%)^-2 + \$15,000(1+12%)^-4
PV = \$5,800 + \$15,000(0.85734) + 15,000(0.635518)
PV = \$5,800 + \$12,860.08 + \$9,532.77
PV = \$27,192.85
• Oct 21st 2010, 04:55 AM
Wilmer
Quote:

Originally Posted by dexteronline
PV = \$29,000x20% + \$15,000(1+8%)^-2 + \$15,000(1+12%)^-4
PV = \$5,800 + \$15,000(0.85734) + 15,000(0.635518)
PV = \$5,800 + \$12,860.08 + \$9,532.77
PV = \$27,192.85

Not quite; the 2nd \$15,000 needs to be discounted at both rates; this way:

PV = .20(29000) + 15,000(1.08^-2) + 15,000(1.12^-2)(1.08^-2) = 28912.06