00:01
Okay, we are told that $5 ,000 becomes $20 ,000 in 10 years if we're compounding semi -annually, which means twice a year.
00:11
And the first thing we do is find the interest rate.
00:14
Now the formula for compound interest is this.
00:17
A is the end amount.
00:19
P starting amount.
00:21
1 plus.
00:23
R is the interest rate in decimal form.
00:27
N number of times you compound per year.
00:30
And t number of years.
00:33
So here i know a, p, n and t which means i can find r.
00:40
So the end amount is $20 ,000.
00:44
P starting amount is 5 ,000.
00:49
One plus r i want to find.
00:52
I'm compounding semi -annually which means twice a year so n is 2.
00:57
And here we have 2 and t number of years which is 10.
01:01
So divide both besides by 5 ,000, so i get 4 on the right is 1 plus r over 2 power of 20, 2 times 10.
01:16
So that means then 4 to the power of 1 over 20 is 1 plus r over 2.
01:25
So with a calculator let's work out 4 power of 1 divided by 20 and that becomes 1 1 .07 -1773, that should be enough equals 1 plus r over 2.
01:48
So we take away 1 from both sides and then times by 2 to find the r value.
01:55
So subtract 1 on the calculator and multiply by 2...