00:01
In this question, we'll be using the compound interest formula.
00:05
A is equal to p times 1 plus r whole n to the power nt.
00:11
Where a is the amount, that is the principal sum plus interest.
00:16
P is the principal sum.
00:18
R is the interest rate per annum in decimal.
00:22
N is the number of times interest is compounded per year.
00:26
And t is the time period in years.
00:29
In this question, we're given a loan of $31 ,000 is made.
00:34
So, we're given that p is the principal sum, is $31 ,000.
00:43
The loan is made at 7 .75 % compound interest compounded annually.
00:51
That is r is 7 .75%.
00:56
Now, divide by 100 % and get the decimal.
00:58
That will be 0 .0775.
01:02
Now, it's compounded annually.
01:04
That is n, the number of times interest compounded per year, will be 1.
01:13
We want to find the number of years it will take where the amount due will reach $51 ,000 or more.
01:27
That is a greater equals to $51 ,000.
01:35
That is what we want to find.
01:42
So, we have a greater equals to $51 ,000...