Nina deposits 500$ into a saving account that earns an annual 5 percent interest. How many years will it take for the amount in the account to double if no additional withdrawals or deposits are made?

Question

Nina deposits 500$ into a saving account that earns  an annual 5 percent interest. How many years will it take for the amount in the account to double if no additional withdrawals or deposits are made?

tkhunny · Answer

There is insufficient information.  Is it simple interest or compound interest?  If compound, is the compounding annual or something else?

anonymous · Answer

compound

tkhunny · Answer

What information have you concerning Compound Interest?  Shall we pull out the Rule of 72s or shall we calculate it directly after you answer the question about the period of the compounding?

anonymous · Answer

annually

anonymous · Answer

idk what that is but is it possible to calculate it using the geometric sequence?

tkhunny · Answer

A geometric series would be great for multiple, regular deposits.  Just one deposit is easier.
$$$500*(1.05)^{n} = 2*($500)$$
Solve for 'n'.

anonymous · Answer

why is it to the n power and not n-1?

tkhunny · Answer

If it takes one (1) year, would it be zero (0)?  No.

anonymous · Answer

what would the question have to be for it to have n-1? The general geometric seq formula confuses me a bit here

kropot72 · Answer

The compound interest formula to use for this problem is:
$$A=P(1+r)^{t}$$
Where A is the amount after time t, P is the principal, r is the annual interest rate as a decimal and t is the time in years.
For the principal to double the formula is rearranged as follows:
$$\frac{A}{P}=2=(1+r)^{t}$$
Now just solve for t

tkhunny · Answer

Forget about the series formula.  Think through the Basic Principles of what you are trying to do.  You are accumulating a single payment for some number of years.  There is nothing to add up.  There is no series.

Note:
This is a Sequence: A, B, C, D, ...
This is a Series: A + B + C + D + ...

Better terminology helps everyone communicate better.

anonymous · Answer

got it thank you! you have answered everything I was looking for :D. and kropot i think i understand tk's way better but thank you anyway :)

kropot72 · Answer

@Ventricate The ways are actually the same!

tkhunny · Answer

Well, they were exactly the same.  Just divide mine by $500.00.  :-)

anonymous · Answer

yea i guess lol but i could never remember that formula under a stressful testing environment :x