Question

An engineering firm invests $100,000 at time zero and $200,000 at the end of year one in an engineering project. Starting from the end of the third year, the engineering project generates a benefit 4 per year. At the end of the 14th year, the investments are fully recovered. The interest rate is 2.18% per month.

(A) What is the nominal interest rate per year (r)?
(B) What is the effective interest rate per year (iₐ)?
(C) Calculate A.

Answer 1

The nominal interest rate per year (r) is 2.89%, the effective interest rate per year (iₐ) is 34.91%, and the final answer (A) is $154,216.12.

Step-by-step explanation:

The nominal interest rate per year (r) can be calculated using the formula:

r = ((A/P)^(1/n)) - 1

Where A is the future value, P is the present value, and n is the number of compounding periods.

In this case, the present value is $100,000, the future value is $300,000, and the number of compounding periods is 14 (since the investment fully recovers at the end of the 14th year).

Plugging these values into the formula gives:

r = ((300,000/100,000)^(1/14)) - 1 = 0.0289, or 2.89%.

The effective interest rate per year (iₐ) is calculated using the formula iₐ = (1 + r)^n - 1.

In this case, the nominal interest rate (r) is 0.0289 and the number of compounding periods (n) is 12 (since the interest rate is given per month).

Plugging these values into the formula gives:

iₐ = (1 + 0.0289)^12 - 1 = 0.3491, or 34.91%.

The final answer (A) can be calculated using the formula A = P(1 + iₐ/n)^(n*t).

In this case, the present value (P) is $100,000, the interest rate per compounding period (iₐ/n) is 0.0289/12, the number of compounding periods (n) is 12, and the number of years (t) is 14 - 3 = 11.

Plugging these values into the formula gives:

A = 100,000(1 + (0.0289/12))^(12*11) = $154,216.12.