Understanding how to do money problems?

[sparater]

4. In 1950, Family A borrowed 100 grams of gold from Family B with an
interest (in gold) of 7%, compounded annually at the end of the year.
Every January 1st, Family A pays o half of what it owes Family B.
(a) How much gold will Family A eventually give back to Family B?
(b) How much gold was paid back by March 2007?
(c) When will Family A be done paying this loan?

 

[I like Serena]

4. In 1950, Family A borrowed 100 grams of gold from Family B with an
interest (in gold) of 7%, compounded annually at the end of the year.
Every January 1st, Family A pays o half of what it owes Family B.
(a) How much gold will Family A eventually give back to Family B?
(b) How much gold was paid back by March 2007?
(c) When will Family A be done paying this loan?

Welcome to MHB, sparater! :)

Perhaps you can indicate where you are stuck?

Let me start by giving a couple of hints in the form of questions.

How much gold will family A owe by December 31st, 1950?
How much gold will family A owe by January 1st, 1951?
How much gold will family B have received by January 1st, 1951?
How much gold will family A owe by December 31st, 1951?
How much gold will family A owe by January 1st, 1952?
How much gold will family B have received by January 1st, 1952?

See a pattern?

 

[sparater]

Thanks for the quick reply!

I am unsure how to start the problem. I don't know what equation and what variables to use!

 

[I like Serena]

Thanks for the quick reply!

I am unsure how to start the problem. I don't know what equation and what variables to use!

Let's worry about equations and variables later.
Perhaps you can start with my suggested questions?

Or if you really want variables, let's pick $n$ for the number of years since January 1st, 1950, $A$ for the amount that family A owes in any year, and $B$ for the amount family B has received in total in any year.

 

[sparater]

I understand that this would be a geometric series problem along with compounding.

I have :

Sum from 0 to infinity of (.465(100*.535^n))

 

[I like Serena]

I understand that this would be a geometric series problem along with compounding.

I have :

Sum from 0 to infinity of (.465(100*.535^n))

Yes, the total that B receives would be a geometric series.
But... where did the factor .465 come from?

Anyway, is there anything in particular that you need help with?
I prefer not to guess as that tends to be counter productive.