00:01
Hi, from the question given that, suppose if you make a monthly payment of dollar 578, that is p is equal to dollar 578, this is a monthly payment into an ordinary annuity earning and interest rate of r is equal to 4 .43 percentage which can be written as 0 .0443.
00:30
Here the interest rate is compounded monthly.
00:34
So here we need to calculate how much will you have in the account after three years.
00:39
So if t is equal to three years, then n is equal to since the interest is compounded monthly, therefore three times of 12, which is equal to 36.
00:55
Hence we know that the formula for future value of an annuity, that is future value of an annuity is p times of 1 plus r the old power n minus 1 divided by r.
01:16
Now substitute the given value so we obtain future value of an anvity is p is 578.
01:27
Times of 1 plus r is 0 .043 the old power n is 36 divided by 0 .0 443 this is minus 1 so simplify this further so this is equal to 578 times of 84 .90135 divided by 0 .90135 divided by 0 .0 .0 .0 .0 .0 .0 .0 .0.
02:01
Double 4 3 so again simplify this 578 times so again simplify it further we obtained 5778 times of 3 .76 1 1 3 divided by 0 .0 243 so simplify this again 578 times 84 .9013 535 so multiply this we obtain 490135 so multiply this we obtain 490 072 .98.
02:40
Hence we conclude that the future value of an annuity after three years will be future value is 49072 .98 dollars.
02:56
Now similarly we need to find the future value of an annuity when the t is equal to eight years...