4. John Payer, owner of Payer's Garage, estimates he will need $55,000 for

new equipment in 8 years. John decided he would put aside the money now

so that in 8 years the $55,000 will be available. His bank offers him 8%

interest compounded semiannually. How much will John invest today so his

account will have $55,000 in 8 years? Check your answer.

29365

Explanation:

Compound interest means that the interest you earn each year is added to your principal, so that the balance doesn't merely grow, it grows at an increasing rate, therefore John needs to put aside today $29.365 as a compound interest rate of 8% will yield as follows:

Year = Principal+interest=New Balance/Principal

Year 1: $29,365 + $2,396 = $31,761

Year 2: $31,761 + $2,591 = $34,352

Year 3: $34,352 + $2,803 = $37,156

Year 4: $37,156 + $3,031 = $40,188

Year 5: $40,188 + $3,279 = $43,467

Year 6: $43,467 + $3,546 = $47,014

Year 7: $47,014 + $3,836 = $50,850

Year 8: $50,850 + $4,149 = $55,000