Question

An investment in a lease offers returns of ​$2200 per month due at the beginning of each month for three years. What investment is justified if the returns are deferred for three years and the interest required is 5​% compounded quarterly​?

An investment of ​$ _____ is justified.

Answer 1

Quarterly rate = 5% / 4 = 1.25%

(1 + quarterly rate)^n - 1 = (1 + monthly rate)^n - 1

(1 + 0.0125)^4 - 1 = (1 + monthly rate)^12 - 1

1.050945 - 1 = (1 + monthly rate)^12 - 1

1.050945 = (1 + monthly rate)^12

Monthly rate = 0.004149 or 0.4149%

Number of periods = 3 * 12 = 36

Present value = (1 + r) * Payments * [1 - 1 / (1 + r)^n] / r

Present value = (1 + 0.004149) * 2200 * [1 - 1 / (1 + 0.004149)^36] / 0.004149

Present value = 1.004149 * 2200 * [1 - 0.861522] / 0.004149

Present value = 1.004149 * 2200 * 33.3763

Present value = $73,732.51

Investment is $73,732.51