Question

Two payments of $16,000 and $3,200 are due in 1 year and 2 years, respectively. Calculate the two equal payments that would replace these payments, made in 6 months and in 4 years if money is worth 5% compounded quarterly.

Answer 1

Answer;

Equal Payment = $10,094.47

Explanation:

Present value in alternative 1

Present value formula = FV x (1+R)^-n

Fv = future value

R = Rate

N = no of compounding period

Present value of $16000

Fv = $16000

Rate =5% per annum

= 5%/4 quarters = 1.25% per quarter

N = 1 year = 4 quarters

Pv = $16000 x (1.0125)^-4

= $16000 x 0.951524

= $15,224.39

Pv of $3,200

Rate = 1.25% per quarter

Period = 2 year = 8 quarters

Fv = $3200

Pv = $3200 x (1+1.25%)^-8

Pv = $3200 x 0.905398

Pv = $2897.28

Net present value of 2 future payments = $15,224.39 + $2,897.28 = $18,121.67

Alternative 2

Present value of 2 equal future payments = $18,121.67

Equal payment = P

So,

6month payment

n = 6 month = 2 quarters

4 year payment

n = 4 years = 16 quarters

PV = P x (1 + R)^-2 + P x (1+ R)^-16

$18,121.67 = P x (1+1.25%)^-2 + P x (1+1.25%)^-16

$18121.67 = P x 0.97546105775 + P x 0.81974634655

$18121.67 = P x 1.7952074

P = $18121.67 / 1.7952074

Equal Payment= $10,094.47

I am trying to help you out with all my effort and heart. Please don’t forget, to like the answer if it was helpful. It keeps me Motivated.