Eliot agreed to pay Julia 4500 plus interest at 8 compounded

Eliot agreed to pay Julia $4,500 plus interest at 8% compounded quarterly in 1 year and 6 months from now. 1 year later, Julia needs substantial liquidity and decides to sell the contract to Fiona Chatwin to yield a rate of return of 10% compounded monthly. What price did Julia receive for the contract? Better with timeline

Solution

Given Data:

Base value or Face value of the loan (P) = $4500

Interest rate (r) = 8% Compounded quarterly.

Tenure (t) = 1.5 years or 1 year 6 months

Compounded value at the end of the tenure, A = P*(1+r/4)^{^6}

= $4500(1+(0.08/4))^⁶

= $5067.73

Required rate of yield for Fiona Chatwin = 10% compounded monthly

Let Price received by Julia be ‘X’,

Therefore,

= $5067.73 = X (1+(r/2))^¹⁸      …….Note (1)

Solving the above equation,

= $5067.73 = X (1+(0.1/12)^¹⁸

= X = $5067.73 / (1+(0.1/12)^¹⁸

= X = $4364.55

Answer:

If Fiona Chatwin wants 10% yield compounded monthly, Julia will receive $4364.55 for the contract.

Note: 12 months in a year multiplied by 1.5 years = 18