You get a loan for $100,000 today and will pay it back with yearly payments of $10,000 each year in years 1 to 10. In addition, you will make a single dollar payment in year 3. How big must the single payment be, if the loan charges 6.00% APR (compounded annually)

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andromache andromache · Answer 1 · 2020-03-05T08:19:21+01:00

Answer:

$31,442

Explanation:

The computation is shown below:

Years Cash flows Discount factor Present value

0 $100,000.00 1 $100,000.00

1 $10,000.00 0.9433962264

2 $10,000.00 0.88999644

3 0.839619283

4 $10,000.00 0.7920936632

5 $10,000.00 0.7472581729

6 $10,000.00 0.7049605404

7 $10,000.00 0.6650571136

8 $10,000.00 0.6274123713

9 $10,000.00 0.5918984635

10 $10,000.00 0.5583947769

Total 7.3600870514

Now the present value is

= $10,000 × 7.3600870514

= $73,600.87

The single payment is

= $100,000 - $73,600.8705

= $26,399.1295

After considering the 6% APR, it is

= $26,399.1295 ÷ 0.839619283

= $31,441.72

The discount factor should be computed below

= 1 ÷ (1 + rate) ^ years

where,

rate is 6%

Year = 0,1,2,3,4 and so on