Question

Determine the value of Q for the cash flow in the figure below with different interest rates as indicated over a period of 4 years. You can leave your answer either in notational form or derive the exact value of Q.

( i1=16%, i2=12)

il % interest 12 % interest compounded compounded semi-annually quarterly

Answer 1

Part 1) We have the following information

Interest rate (i) = 16% compounded semi-annually

No. of interest periods per year, (C) = 2

Effective interest rate (R) = ((1 + (i/C))^C – 1

R = ((1 + (16%/2))² – 1

R = 16.64% compounded annually

Present Worth = 250(P/F, 16.64%, 1) + 100(P/F, 16.64%, 2) + 100(P/F, 16.64%, 3) + 250(P/F, 16.64%, 4)

Present Worth = 250/(1 + 0.1664)¹ + 100/(1 + 0.1664)² + 100/(1 + 0.1664)³ + 250/(1 + 0.1664)⁴

Present Worth = 214.33 + 73.50 + 63.02 + 135.07

Value of Q is 485.92

Part 2) We have the following information

Interest rate (i) = 12% compounded quarterly

No. of interest periods per year, (C) = 4

Effective interest rate (R) = ((1 + (i/C))^C – 1

R = ((1 + (12%/4))⁴ – 1

R = 12.55% compounded annually

Present Worth = 250(P/F, 12.55%, 1) + 100(P/F, 12.55%, 2) + 100(P/F, 12.55%, 3) + 250(P/F, 12.55%, 4)

Present Worth = 250/(1 + 0.1255)¹ + 100/(1 + 0.1255)² + 100/(1 + 0.1255)³ + 250/(1 + 0.1255)⁴

Present Worth = 222.12 + 78.94 + 70.14 + 155.80

Value of Q is 527.00