Jaime owes Eddie $12,000 at the end of 3 years and $18,000 due at the end of...

Jaime owes Eddie $12,000 at the end of 3 years and $18,000 due at the end of 7 years with accumulated interest from today at 10% compounded quarterly. Jaime decided to settle his obligations by making a payment of $8,000 at the end of year 1, $5,000 at the end of year 5 and another payment at the end of year 9. if they agree that money is worth 14% compounded semi-annually, find the size of the payment at the end of 9 years?

Solutions

Expert Solution

At the end of 7 years, Jaime owes Eddie $18,000

Jamie pays $8,000 in first year, $5,000 in 5th year and rest in 9th yea at rate of interest 14% compounded semi - annually.

Interest rate compounded semi annually is 14% / 2 = 7% = 0.07

Future value using semi annual interest rate is P (1 + 0.07)n * 2 where n is number of years and it is multiplied by 2 to get twice compounding in an year.

Till first year, $18,000 would become 18,000 [1 + 0.07]2 = $20,608.2

Payment in first year is $8,000 which makes pending payment equal to $20,608.2 - $8,000 = $12,608.2

Till 5th year, this $12,608.2 will get rate of interest which will make it $12,608.2 (1 + 0.07)8 = $21,663.23

Payment made in 5th year is $5,000 which makes rest of the payment = $21,663.23 - $5,000 = $16,663.23

Till 9th year, this $16,663.23 will get rate of interest which will make it $16,663.23 (1 + 0.07)8 = $28,630.53

In 9th year, Jamie have to pay $28,630.53

Rahul Sunny answered 1 month ago

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