Question

Joe must pay liabilities of 2000 due one year from now and another 1000 due two years from now. He exactly matches his liabilities with the following two investments: Mortgage I: A one year mortgage in which X is lent. It is repaid with a single payment at time one. The annual effective interest rate is 6%.Mortgage II: A two-year mortgage in which Y is lent. It is repaid with two equal annual payments. The annual effective interest rate is 7%. Calculate X + Y.

Answer 1

$2,760.23

Step-by-step explanation:

As X and Y is the mortgage value, and we need to calculate it by using following formula

FV = PV x ( 1 + r )^n

PV = FV / ( 1 + r )^n

First we will calculate the X

Where FV =Future Value = 2,000

r = Annual effect interest rate = 6%

n = numbers of periods = 1 Year

By Placing values in the formula

PV = $2,000 / ( 1 + 6% )^1

PV = $1,886.79

Now we will Calculate the Y

Where FV =Future Value = 1,000

r = Annual effect interest rate = 7%

n = numbers of periods = 2 Year

By Placing values in the formula

PV = $1,000 / ( 1 + 7% )^2

PV = $873.44

As we need to calculate

X + Y = ?

So,

X + Y = $1,886.79 + $873.44 = $2,760.23

Answer 2

The value of X+Y=2,769

Step-by-step explanation:

According to the given data we have the following:

x=present value of 2,000

=2,000/(1+0.06)=1,886.79

y=present value of 1,000

=1,000(1+0.07)∧2=873.44

x+y=1,886.79+873.44

=2,760.23

=2,769

The value of X+Y=2,769