Question

Sandler invested an average of $275 per month since age 45 in various securities for his retirement savings. His investments averaged a 2.5% annual rate of return until he retired at age 72. Given the same monthly investment and rate of return, how much more would Sandler have in his retirement savings had he started investing at age 35? Assume monthly compounding.

$89,749.64

$118,387.50

$82,500.00

$73,496.08

Answer 1

You use this simple equation, you have the variables, just plug it in

A = P(1 + r)n

P is the principal (the initial amount you borrow or deposit)

r is the annual rate of interest (percentage)

n is the number of years the amount is deposited or borrowed for.

A is the amount of money accumulated after n years, including interest.

When the interest is compounded once a year:

Answer 2

P = 275
R=0.025
N=12 ???

Answer 3

No, do not use that Single Payment formula. You need a periodic payment formula.

Answer 4

@NaCl You have to step up and start having a better clue in these things.

What have you tried?
What tools are at your disposal?
Does this look at all like any other problem you have solved?

I really want to slap the author of so many problems:
"an average of $275 per month"
"investments averaged a 2.5% annual rate of return"

That's really not quite enough information to answer:

"how much more would Sandler have"

275 275 275 275 -- Average 275
0 0 0 1100 -- Average 275
1100 0 0 0 -- Average 275

It's just not enough information.

Answer 5

I tried but I don't know how to attack this problem :/ 9,9

Answer 6

Do you have an accumulation formula?

I = 0.025 -- Annual Interest Rate
j = i/12 -- Monthly Interest Rate
r = 1+j -- Monthly Accumulation Factor

72 - 45 = 27
72 - 35 = 37

Starting at 47

275(1 + r + r^2 + ... + r^(27*12 - 1)) = \(275\cdot\dfrac{1 - r^{324}}{1-r}\)

Starting at 37

275(1 + r + r^2 + ... + r^(37*12 - 1)) = \(275\cdot\dfrac{1 - r^{444}}{1-r}\)

If you learn Basic Principles, you will never again fail to know how to attack a problem. I continue to be stunned that no one seems interested in this information.

Answer 7

* Starting at 45
* Starting at 35

Answer 8

So keep plugin it in the formula ?

Answer 9

No, there is no such thing as "plugging in". Please feel free to substitute appropriate values for your particular problem statement,

What I actually said was "learn Basic Principles".

Once you have the two accumulated values, you will not be done. Read the problem statement again.