Question

At what rate of interest per annum will an amount get doubled in 16 years?
A- 12%
B- 8%
C- 15%
D- 25/4%

Answer 1

Here's a formula
log(1 + rate) = {log(total) -log(Principal)} ÷ Years
Don't be intimidated.

Let's say the total is 2 and the principal is 1 and years = 16
log (1+rate) = log(2) - log(1) / 16
log(1 + rate) = (0.3010299957 - 0) /16
log(1 + rate) = 0.0188143747

10^0.0188143747 = 1 + rate
1.0442737824 = 1 + rate
.0442737824 = rate
or rate = 4.42737824

Answer 2

I got the formula from here:
http://www.1728.org/compint2.htm

And to check that answer, there's a formula and a calculator here:
http://www.1728.org/compint.htm

Total = Principal * (1 + rate) ^ years
2 = 1 * (1.0442737824)^16

2 = 2

It checks

Answer 3

but 2 is not in their options

Answer 4

which one is right?

Answer 5

No 2 is not the answer.
The RATE is 4.42737824
which is close to D 25/4

Answer 6

Wait that comes to 6.25 %
Let me recheck that

Answer 7

http://skillgun.com/question/4814/arithmetic/simple-interest/at-what-rate-percent-per-annum-will-a-sum-of-money-double-in-16-years
in this link have similar question but ans process is not in their

Answer 8

The formula for compound interest is
Total = principal * (1+rate)^years
we need the total to be twice what we started with so let's say total = 6 and principal =3

6 = 3 * (1.0442737824)^16

6 = 5.9999999975

Close enough don't you think?

Answer 9

but which one i choose the option

Answer 10

The formula they use isn't the correct one

Answer 11

Do you have access to an online compound interest calculator so you can try 6.25% to see that it is INCORRECT?

Answer 12

ya i was try thats incorrect?

Answer 13

I found one here:
http://www.moneychimp.com/calculator/compound_interest_calculator.htm
My answer 200 at 6.25% interst produces an answer of 527.59
That should be $400 but it isn't

Answer 14

I went to that calculator and used $200 for 16 years at 4.42737824% and my answer was $400.16

Seems as if I'm right.
I could find another calculator.

Answer 15

Here's another online calculator
http://www.calculatorsoup.com/calculators/financial/compound-interest-calculator.php
I input $100
4.42737824% rate
and 16 years

answer was $200.00

Answer 16

answer is D

**simple** interest at rate r for 16 years on amount X equals 16 * r * X
set that to X to double the original amount ie

solve 16 * r * X = X
=>> r = 1/16 = 100/16 % = 25/4%

the 4.43% is if interest is compounded in which case you are solving this for r

Answer 17

this!

\[X (1+r)^{16} = 2X\]

Answer 18

Where are you getting that formula?

Answer 19

which formula??

if you mean for **compounded** interest , it is just this
start amount X
after period 1 X(1+r)
after period 2 X(1+r)(1+r) = X (1+r)^2
after period 3 X(1+r)(1+r)(1+r) = X (1+r)^3
and so on

it's really that simple.

Answer 20

You mean this is SIMPLE interest?
Geez, I'm so used to solving compound interest problems.
(They are a "tad" more difficult).

Answer 21

but the question is about simple interest so you just add up all the interest as its earned, but you never add it to the interest bearing original amount

so 16 * r * X = X

Answer 22

@wolf1728
yes mate

it should have been stated in the question. your solution is sound but addresses a more complex question!

Answer 23

Yes, I understand simple interest. This is the FIRST time I even saw a simple interest question here.

Answer 24

yes thanks to all

Answer 25

okay