# Business MathUnderstanding how to do money problems?

#### sparater

##### New member
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?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
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

##### New member

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

#### Klaas van Aarsen

##### MHB Seeker
Staff member

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.

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

##### New member
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))

#### Klaas van Aarsen

##### MHB Seeker
Staff member
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.