Question

A mortgage requires you to pay $70,000 at the end of each of the next eight years. The interest rate is 8%.

Answer 1

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%

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 70,000.00

time 8

rate 0.08

$70000 \times \frac{1-(1+0.08)^{-8} }{0.08} = PV$

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