1) How many years will it take $5,000 to double at an interest rate of 8% per ye

Question

1) How many years will it take $5,000 to double at an interest rate of 8% per year, compounded annually? If the interest rate is only 4%, how many years will it take to double?

2) Calculate the future value of the following investments at an effective interest rate of 12% per year.

a) $800 invested at the end of each of the next eight years.

b) $400 invested every six months for the next eight years.

c) $600 received at the end of each of the following four years and $1000 per year for the four years thereafter.

d) $75 invested monthly for the next eight years.

3) Calculate the present value of the cash flows for each part of problem (2).

4) An oil producer has purchased a pumping unit for $30,000 and the loan is to be paid back in 24 equal monthly installments of $1,586.13 per month. a) Calculate the nominal interest rate charged on this financing agreement. b) Calculate the effective interest rate.

5) An oil company has installed an offshore production facility for $10 million in year 1. The annual maintenance cost of the facility is $60,000 per year for the 2nd year, increasing by $10,000 per year for the next 9 years. In the 12th year, a major overhaul is conducted at a cost of $500,000. The overhaul helped in keeping maintenance costs fixed at $150,000 per year for the remaining 10 years. At the end of 22 years, the facility is sold for a sum of $2 million. If the market interest rate is 8% per year, calculate the present value at year 0 of all the costs over the 22- year period.

Note: all expense are to be assumed to incurred at the end of year specified.

Please even when full working is shown, i would also love to see the cash flow plots using Excell or any other software(Excell preferrably). Thanks

Explanation / Answer

(1)

(a) If doubling period be N years, then

$5,000 x (1.08)N = $5,000 x 2

(1.08)N = 2

Taking natural logarithm on both sides,

N x ln 1.08 = ln 2

N x 0.0770 = 0.6931

N = 9 years

(b) If doubling period be N years, then

$5,000 x (1.04)N = $5,000 x 2

(1.04)N = 2

Taking natural logarithm on both sides,

N x ln 1.04 = ln 2

N x 0.0392 = 0.6931

N = 17.67 years

NOTE: As per Answering Policy, 1st question has been answered.

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