Question

Two payments of $13,000 and $7,300 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 6% compounded quarterly.

Answer 1

- Two payments of $13,000 and $7,300 are due in 1 year and 2 years, respectively

calculating the Present value today of these payments:-

Where, Payment1 = Payment in year 1 = $13,000

n = No of periods of payment 1 = 1 year*4 = 4

r = Periodic Interest rate = 6%/4 = 1.5%

Payment2 = Payment in year 2 = $7300

m = No of periods of payment 2 = 2 year*4 = 8

Present Value = $12248.39 + $6480.29 = $18,728.68

Present Value of two paymnets is $18,728.68

Now, Lets us assume the equal payments in 6 months and in 4 years is X

Compauting the Equal paymnets:-

where, Present Value = $18,728.68

r = Periodic Interest rate = 6%/4 = 1.5%

n = No of periods of payment 1 =0.5 year*4 = 2

m = No of periods of payment 2 = 4 year*4 = 16

X = $10,649.20

So, the two equal payments that would replace these payments is $10,649.20

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating