A find the payment necessary to amortize the following loan...

A ) Find the payment necessary to amortize the following loan. $7700; 8.8% compounded semiannually; 24 semiannual payments The payment is B) Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance. Twenty-year mortgage for $220,000 at 3.66%; remaining balance after 12 years. The monthly payment is

Transcript

00:01 Hi, in the given problem we are required to find the payment necessary to amortize the $77 ,700 at the rate of interest are is equal to 8 .8 % which is compounded semi -annually so n would be two here and this is now 24 semi -annual payments are so the for the 24 semi -annual payments are so the for the 24 semi -annual payments annual payment so t would be 24 now we are be using the amortization formula which says that p is equal to a times one minus one plus r over m to the power minus nm whole divided by i r over m so p is the principle which is this so this is principle p is equal to 7700 r is the rate of interest so this comes out to be 7700 is equal to 8 times and this is what we have to find a so 1 minus 1 plus 0 .088 over 2 because semi -annual minus 12 times 2 whole divided by 0 .08 8 over 2 so from here we get the value of a as approximately equal to five to nine point three seven five dollars so the approximate value is five twenty nine point three seven five dollars so that's the amount and when we are in the next part we are required to find the equated monthly installment so the installment would be p times are formula is p r times 1 plus r to the power n over over 1 plus r to the power n minus 1 so this is 22 220 thousand times 0 .0366 times 1 plus 0 .0366 to the power 20 times 20 times 12 so this is 20 times 12 20 times 12 so this is approximately equal to 8346 .703 so that's the amount that's the monthly installment now the remaining balance after 12 way can be found by finding the total present value of the mi to be paid during the remaining tenure so so that would be let's say the remaining amount is so 8346 .7 times 1 minus 1 plus 0 .0366 over 12 times minus 18 over 12.

03:40 And then whole divided by 0 .0366 over 12.

03:48 So this is approximately $69372723 .139.

03:58 So the remaining balance after 12 years would be this much...

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