# math

Jungle Jim owes three debts:

\$500 due in one year plus interest at 6% compounded semi-annually,
\$2000 due in two years,
\$1000 due in three years plus interest at 5% compounded monthly.

He wishes to discharge these debts by paying \$500 now and two equal but unknown payments in one and two years respectively. Find the size of the equal payments if money is, at present, worth 12% compounded quarterly. Use a focal date of two years.

1. 👍
2. 👎
3. 👁
1. You state different interest rates for the 1st and 3rd debt, but state no rate for the 2nd debt of \$2000 due in 2 years.
Other than , choose a time as a reference or focal date
I picked the present time, so

at present, the value of the debt = value of payments

500(1.03)^-2 + 2000(1+i)^-? + 1000(1.0041666..)^-36 = 500 + x(1.03)^-4 + x(1.03)^-8

once you establish what the second interest rate is, evaluate each part, the x terms can be added.

1. 👍
2. 👎
2. The focal date is 2 years, that is your reference.

Old debt (owing) = New debt (paying)

Old Debt

First part

500*(1 + 0.06/2)^(1*2) - The future value of the first debt

* (1 + 0.12/4)^(1*4) - To move the debt to the two year focal date. Move focal date + 1 year. Note we use the rate 12% compound quarterly to move it to the focal date as that is what the money is worth now.

Second part

Just leave it a \$2000. This debit is already at the focal date. That is why no interest rate is given.

Third part

FV = 1000*(1+0.05/12)^(3*12) - The future value of the third debt

* (1 + 0.12/4)^(-1*4) - To move the debt to the two year focal date. Move focal date - 1 year.

To put the old debt all together:

Old Debt = 500(1+0.06/2)^(1*2)*(1+0.12/4)^(1*4) + 2000 + 1000(1+0.05/12)^(3*12)* (1 + 0.12/4)^(-1*4)

Old Debt = 500(1.03)^2*(1.03)^4 + 2000 + 1000(1.004166667)^36*(1.03)^-4

Old Debt = \$3,628.979182

New Debt (Paying) x = payment amount

500(1*0.12/4)^(2*4) - \$500 is paid now, add +2 to get it to the focal date

x(1+0.12/4)^(1*4) - A payment is made in 1 year, add +1 to get it to the focal date

x - Just add x. Payment is at focal date

So, we get

New debt = 500(1*0.12/4)^(2*4) + x(1+0.12/4)^(1*4) + x

New Debt = 500(1.03)^8 + x(1.03)^4 + x

Old Debt = New Debt

\$3,628.979182 = 500(1.03)^8 + x(1.03)^4 + x

Solving for x gets you x = \$1,409.35

So, the size of each payment is \$1,409.35

1. 👍
2. 👎

## Similar Questions

1. ### Social studies

What part of the offered deal is the interest rate... A. 2 year term B. Up to \$40,000 C. 6% compounded annually D. \$500 up front payment

2. ### Algebra

Car financing for less 2-year term Up to \$40,000 6% compared annually with a \$500 up-front payment 1. What part of the offered deal is this interest rate? 2 year term Up to \$40,000 6% compounded annually**** \$500 up-front payment

3. ### Finance

Danny Joe borrows \$10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is: \$_________. (Please calculate the arithmetic solution and

4. ### Math

A boat costs \$92,000 and depreciates in value by 15% per year. How much will the boat be worth after 10 years? 18,112.45 78,200 18,941.98 69,000 18,112.45 A \$6000 principal earns 8% interest compounded semi annually after 35

1. ### Math

Jim Hunter decided to retire to Florida in 10 years. What amount should Jim invest today so that he will be able to withdraw \$25,000 at the end of each year for 30 years after he retires. Assume he can invest money at 9% interest

2. ### Mathematics

Find the amount and the compound interest on rs 12800 for 1 year at 15/2 percent per annum compounded semi annually

3. ### Accounts

Present value of Rs.2000 due in 6 years if money is worth compounded semi annually

4. ### engineering economics

A) A company has issued 10-year bonds, with a face value of \$1,000,000 in \$1000 units. Interest at 8% is paid quarterly. If an investor desires to earn 12% nominal interest (compounded quarterly) on \$10000 worth of these bonds,

1. ### Math

If \$6,700 is invested at 4.6% interest compounded semi-annually, how much will the investment be worth in 15 years?

2. ### Math

you deposit \$1000 at 3% per year.what is the balance at the end of one year,and what is the annual yield,if the interest.Please help solve the problem. Simple interest? Compounded annually? Compounded quarterly Compounded daily

3. ### Math

Deana invests some money that earns interest compounded annually. At the end of the first year, she earns \$400 in interest. At the end of the second year, she earns \$432 in interest. a) what interest rate, compounded annually, is

4. ### Math

Sara buys a washer and a dryer for \$2112.She pays \$500 and borrows the remaining amount. A year and a half later she pays off the loan, which compounded semi-annually, was Sara being charged.