Question

Oxygen Optimization just bought a new filtration system for 167,300 dollars. To pay for the filtration system, the company took out a loan that requires Oxygen Optimization to pay the bank a special payment of 101,000 dollars in 5 year(s) and also make regular annual payments forever. The first regular payment is expected in 1 year and is expected to be 1,800 dollars. All subsequent regular payments are expected to increase by a constant rate each year forever. The interest rate on the loan is 15.48 percent per year. What is the annual growth rate of the regular payments expected to be? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer #2

A | Amount of loan | $167,300 | ||

B | Special payment after 5 years | $101,000 | ||

C | Interest rate=15.48%= | 0.1548 | ||

D=B/((1+C)^5) | Present Value of Special payment | $ 49,179.88 | ||

E=A-D | Balance amount of Loan | $118,120.12 | ||

F | First Instalment to be paid year1 | $1,800 | ||

g | Rate of growth of payment=g | |||

Present Value of annual payment: | ||||

P0 | P0=F/(C-g) | |||

P0 | P0=1800/(0.1548-g)=$118,120.12 | |||

0.1548-g=1800/118120.12= | 0.015238725 | |||

g=0.1548-0.15238725= | 0.139561275 | |||

Annual Growth Rate | 0.1396 | |||

answered by: anonymous

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