Question

Course: Theory of Interest

You are purchasing a TV and can pay for it in two ways,

a) $50000 now and an additional $50000 in three years

b) $80000 now

At what interest rate are these two methods equivalent?

How do I solve this both manually and using the TI-BA II Plus Professional Calculator?

Answer: 14.796%

Answer 1

The present value of method (a) should be equal to method (b)

80,000 = 50,000 + 50,000 / (1 + i)³

50,000 / (1 + i)³ = 80,000 - 50,000 = 30,000

(1 + i)³ = 50,000 / 30,000 = 1.667

1 + i = cube root of 1.67

1 + i = 1.18571

i = 1.18571 - 1 = 0.18571   or 18.571%

At 18.571 interest rate, these two methods are equivalent