Finding the initial investment for saving for college

[AJ.Interrante]

The problem is: In 18 years a family will need about $134,000 for a college education. If the account they invest in earns a 6 percent simple interest, how much money must they invest now to cover the cost of the college education? I played around with the numbers until I figured it out, but I know there has to be a simpler formula for figuring this out. I know that Interest = Principal x rate x term and that Principal + Interest = $134,000. I know the answer is: $64,423.08
That is all I can figure out. Thanks for your help and interest (no pun intended!) Have a great day!

 

[Deleted member 4993]

The problem is: In 18 years a family will need about $134,000 for a college education. If the account they invest in earns a 6 percent simple interest, how much money must they invest now to cover the cost of the college education? I played around with the numbers until I figured it out, but I know there has to be a simpler formula for figuring this out. I know that Interest = Principal x rate x term and that Principal + Interest = $134,000. I know the answer is: $64,423.08
That is all I can figure out. Thanks for your help and interest (no pun intended!) Have a great day!

For simple interest, amount after a time period,

A(mount) = P(rincipal) + P * r(ate) * t(ime)

In the equation above,

What is the unknown variable (i.e. whose value you need to find)?

what are the known variables (i.e. whose values you know)?

Once you fix that - put those in the equation above and solve for the unknown.

 

[AJ.Interrante]

I neglected to explain that the only reason I know the answer is that I figured it out through trial and error, not because it was provided in the original problem. Therefore, if I pump into the equation the things I know, I don't think I can solve the original problem this way. Here is my new progress:

$134,000 = P + P * .06 * 18

In regards to the 2 "P" s...The first "P" is Principal, but what is the second "P"?

Thanks, again for your help!

 

[Denis]

$134,000 = P + P * .06 * 18
In regards to the 2 "P" s...The first "P" is Principal, but what is the second "P"?

That's correct; second P is same as the first...

P + 1.08P = 134000
P(1 + 1.08) = 134000 : kapish?
2.08P = 134000
P = 134000 / 2.08 = 64,423.07692....

 

[AJ.Interrante]

Ahhhhhhh, now I get it. Is this just one of those formulas to memorize? I appreciate your help and "investment of your time".

 

[rontrengove]

I still don't understand the value of 1 for the P in: P+P*r*t. I understand 1.08P + P, but not sure how we can assume 1 for P to turn it into 2.08P

 

[Deleted member 4993]

I still don't understand the value of 1 for the P in: P+P*r*t. I understand 1.08P + P, but not sure how we can assume 1 for P to turn it into 2.08P

You know
P + 1.08 P = P * 1 + 1.08 * P

You can factor out "P"

= P * ( 1 + 1.08)

= P * 2.08

It is same procedure as

P + 2P ? how much is that?

= P*1 + 2*P

= P* (1 + 2)

= P * 3

 

[mmm4444bot]

I still don't understand the value of 1 for the P

not sure how we can assume 1 for P

P is not 1; the (unwritten) factor in front of P is 1.

There is a factor of 1 in front of the symbol P. It's not explicity shown.

P = 1*P

In fact, there is a factor of 1 in front of all symbols.

x means 1*x

Q means 1*Q

a means 1*a

? means 1*?

et cetera

We do not write the factor of 1 because it does not change anything. We use the factor of 1 mostly when factoring.

Of course, if a negation symbol preceeds a symbol representing some number, then the factor in front is -1 instead of 1.

-x means (-1)(x)

-Q means (-1)(Q)

-a means (-1)(a)

-? means (-1)(?)

et cetera