Question

A payment of $2,300 is due in 2 years and $3,800 is due in 4 years. These two original payments are to be rescheduled with a payment of $1,900 in 1 year and the balance in 3 years. Calculate the payment required in 3 years for the rescheduled option. Assume that money earns 3.25% compounded semi-annually.

Answer 1

Given that,

A payment of $2,300 is due in 2 years and $3,800 is due in 4 years. These two original payments are to be rescheduled with a payment of $1,900 in 1 year and the balance in 3 years.

interest rate r = 3.25% compounded semiannually.

So, comparing the present value of all the payments to calculated the value of payment in year 3.

Present value is calculated using formula

PV = FV/(1+r/n)^(n*t)

here FV is payment size

r is interest rate = 3.25%

n is compounding frequency = 2 for semiannual compounding

t = time period of the payment

-> 2300/(1+0.0325/2)^(2*2) + 3800/(1+0.0325/2)^(2*4) = 1900/(1+0.0325/2)^(2*1) + X/(1+0.0325/2)^(2*3)

=> 3656.9095 = X/0.9078

=> X = 3319.79

So, Payment required in yer 3 is $3319.79