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A mortgage requires you to pay $70,000 at the end of each of the next eight years. The interest rate is 8%.
A. What is the present value of these payments?
B. Calculate for each year the loan balance that remains outstanding, the interest payment on the loan, and the reduction in the loan balance.

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TomShelby

Answer:

PV $402,264.7261

balance of the mortage

1-y from now   $364,445.9041

2-y from now   $323,601.5765

3-y from now  $279,489.7026

4-y from now  $231,848.8788

5-y from now $180,396.7891

6-y from now   $124,828.5322

7-y from now   $64,814.8148

Explanation:

We sovle for the PV of the annuity of 70,00 during 8 years discounted at 8%

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 70,000.00

time 8

rate 0.08

[tex]70000 \times \frac{1-(1+0.08)^{-8} }{0.08} = PV\\[/tex]

PV $402,264.7261

To know the value of the outstanding dbet we can repeat this formula changing the values for time

t = 7   $364,445.9041

t = 6   $323,601.5765

t = 5   $279,489.7026

t = 4   $231,848.8788

t = 3   $180,396.7891

t = 2   $124,828.5322

t = 1   $64,814.8148

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