Calculate the following.
What is the size of the loan that will be paid $1000/wk for 1 year for
a total of 52 payments at an annualized interest of
a: 15%
b: 20%
c: 25%
d: 30%

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Clarification of Question by saintjamesc-ga on 30 Oct 2003 18:51 PST

For extra credit - What if the payments were $200?

Hello.

The formula for calculating the size of the loan is:

L = W / (I/52)/(1-(1+(I/52)^-N)

L is the size of the loan
W is the weekly payment (e.g., $1000 or $200)
I is the interest rate in decimals (e.g., .15, .20, .25 or .30)
N is the total number of payments (e.g., 52)

source:
"How to calculate amortization tables by hand," hosted by interest.com
http://www.interest.com/hugh/calc/formula.html
Formula derivation, hosted by interest.com
http://www.interest.com/hugh/calc/formula_deriv.html

a. 15%: $48,223.47
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=1000%2F%28%28.15%2F+52%29%2F%281-%28%281%2B%28.15%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search

b. 20%: $47,048.32
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=1000%2F%28%28.20%2F+52%29%2F%281-%28%281%2B%28.20%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search


c. 25%: $45,912.37
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=1000%2F%28%28.25%2F+52%29%2F%281-%28%281%2B%28.25%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search

d. 30%: $44,814.10
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=1000%2F%28%28.30%2F+52%29%2F%281-%28%281%2B%28.30%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search


All of these figures may be verified by using Robert's Online Loan
Pricer:
http://www.intrepid.com/~robertl/loan-pricer1.html

Or by using the generic loan calculator at interest.com:
http://www.interest.com/hugh/calc/genloan.cgi

For example, to verify (a) enter:
Loan Amount: 48223.47
Annual Interest: 15
Payment each period: [set to -1 to let calculate]
Periods per year: 52
Total number of payments: 52
[press 'calculate']

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For extra credit:

If the payments were $200...

a. 15%: $9,644.69
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=200%2F%28%28.15%2F+52%29%2F%281-%28%281%2B%28.15%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search


b. 20%: $9,409.66
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=200%2F%28%28.20%2F+52%29%2F%281-%28%281%2B%28.20%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search


c. 25%: $9,182.47
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=200%2F%28%28.25%2F+52%29%2F%281-%28%281%2B%28.25%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search


d. 30%: $8,962.82
Computed using Google calculator:
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=200%2F%28%28.30%2F+52%29%2F%281-%28%281%2B%28.30%2F+52%29%29%5E%28-52%29%29%29%29&btnG=Google+Search

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amortization, calculate "by hand"

I hope this helps.

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Clarification of Answer by juggler-ga on 30 Oct 2003 20:32 PST

I notice that I left out a parenthesis in that formula at the
beginning of the answer. It should have been:

L = W / (I/52)/(1-(1+(I/52))^-N)