Question

A problem about financial math generated by
http://saab.org

Answer 1

So...why can we help you with this?

You need a timeline. That is all.

First Loan (8% Semiannual)
Time 0 - $0
Time 1 - $0
Time 2 - $0
Time 3 - $3000

Second Loan (6% Semiannual)
Time 0 - $0
Time 1 - $0
Time 2 - $0
Time 3 - $0
Time 4 - $4000

Consolidated Loan (11% Semiannual)
Time 0 - $X
Time 1 - $0
Time 2 - $X

Out task is to find the equivalent Present Value of the payment streams as described. It seems most appropriate, simply to discount them to the beginning, where the first $X is due.

First Loan \($3000\cdot (1.04)^{-6} = 2370.94\)
Second Loan \($4000\cdot (1.03)^{-8} = 3157.64\)
Present Value of Present Debt at Time Zero (0) is then 2370.94+3157.64 = 5528.58

Consolidated Loan \($X + $X\cdot(1.055)^{-4} = $X\cdot(1 + 1.055^{-4}) = $X\cdot 1.807217\)

And thus we see that we need $5,528.58 = $X(1.807217)

It is hoped that you can see where to go from there.

Answer 2

Here is my solution generated by http://saab.org

Answer 3

Loan 2 is $6,000 at t=4, otherwise your method is the right one @tkhunny

Answer 4

Personally, I would like to avoid the negative exponents by defining v = (1+i)^(-1) = 1/(1+i). Using v makes the notation much cleaner. Good work.

Answer 5

Ah, well, learning to read is also important. Sorry about that. I must have checked that at least four times. Another pair of eyes never hurts.

Answer 6

Using of v is common in Financial Math