Question

In: Economics

A machine is purchased for $2 million dollars with a monthly loan payment lasting 3 years.

A machine is purchased for $2 million dollars with a monthly loan payment lasting 3 years. With a nominal interest rate at 4%, what is the balance due after 22 months?

Solutions

Expert Solution

Nominal interest rate of 4% per annum will translate to 4%/12 = 0.33% as monthly rate of interest. We can set up a table in Excel to solve it once we know the monthly loan payment. That can be found using the formula for PV of annuity

A = P*((1-(1+r)^-n)/r)

Where

A = $2000000

P = to be found

r = 0.33% per month

n = 36, i.e., 12 months * 3 years

P = $2000000/((1-(1.0033^-36))/0.0033) = $59012.39

Now we can set it up in Excel to find out the balance due after 22 months. It will be 806080.525

Time Machine cost Interest = 0.33% * balance due previous month Monthly payment Balance due = balance due previous month + interest - monthly payment
0 2000000 2000000
1 6600.000 59012.390 1947587.610
2 6427.039 59012.390 1895002.259
3 6253.507 59012.390 1842243.377
4 6079.403 59012.390 1789310.390
5 5904.724 59012.390 1736202.724
6 5729.469 59012.390 1682919.803
7 5553.635 59012.390 1629461.048
8 5377.221 59012.390 1575825.880
9 5200.225 59012.390 1522013.715
10 5022.645 59012.390 1468023.970
11 4844.479 59012.390 1413856.060
12 4665.725 59012.390 1359509.395
13 4486.381 59012.390 1304983.386
14 4306.445 59012.390 1250277.441
15 4125.916 59012.390 1195390.966
16 3944.790 59012.390 1140323.366
17 3763.067 59012.390 1085074.044
18 3580.744 59012.390 1029642.398
19 3397.820 59012.390 974027.828
20 3214.292 59012.390 918229.730
21 3030.158 59012.390 862247.498
22 2845.417 59012.390 806080.525
23 2660.066 59012.390 749728.200
24 2474.103 59012.390 693189.913
25 2287.527 59012.390 636465.050
26 2100.335 59012.390 579552.995
27 1912.525 59012.390 522453.130
28 1724.095 59012.390 465164.835
29 1535.044 59012.390 407687.489
30 1345.369 59012.390 350020.468
31 1155.068 59012.390 292163.145
32 964.138 59012.390 234114.893
33 772.579 59012.390 175875.083
34 580.388 59012.390 117443.080
35 387.562 59012.390 58818.253
36 194.100 59012.390 -0.037

Rahul Sunny answered 2 years ago
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