Calculate the size of the loan payment or deposit.

Hey guys, can someone please check if this answer is correct or did I do any mistake in between .


Ms. Halliday received a mortgage loan from the Bank of Nova Scotia for $60,000 at 11.25% compounded semi-annually for a five-year term. Monthly payments were based on a 20 year amortization period.


Here I am trying to look for the payment...

PV 60,000 n (12)(20) = 240 i 11.25/2=5.625 % c=2/12=0.16

PV= PMT [1-(1+i)^-n /i]
60000=PMT [ 1-(1+0.056 ^-240/0.056 ] = 3360.00

No, no... Interest rate is bad. You MUST make sure your payments and interest are on the same basis.

Your interest is semi-ammual and your payments are monthly. You have to fix that.

Annual Interest: i = 0.1125

Semi-Annual Compounding: \(\displaystyle i^{(2)}\;=\;0.1125/2\)

Monthly Effective Consideration: \(\displaystyle i^{(12)}\;=\;[(1+i^{(2)})^{1/6}]\;-\;1\)

Hi, I just want to make this clearly.. So the interest part is wrong right?? and how did you get the 1/6 part?

...can someone please check if this answer is correct or did I do any mistake in between?

Ms. Halliday received a mortgage loan from the Bank of Nova Scotia for $60,000 at 11.25% compounded semi-annually for a five-year term. Monthly payments were based on a 20 year amortization period.

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The periodic payment, often referred to as the rent, is what must be paid, knowing only the present value, interest rate and the number of payment periods.

Example: What is the periodic payment required to retire a debt of P dollars in n periods (months or years) if payments start at the end of the first period and bear I% interest compounded periodically? For this typical loan payment calculation,

......................R = Pi/[1 - (1 +i)^(-n)]

where R = the rent (periodic payment), P = the amount borrowed, n = the number of payment periods, and i = I/100.

Example: What is the annual payment required to retire a loan of $10,000 over a period of 5 years at an annual interest rate of 8%? Here, P = 10,000, n = 5, and i = .08 resulting in

...........................R = 10000(.08)/[1 - (1.08)^-5] = $2504.56 per year

For your case, the monthly payment required to retire a debt of $60,000 over a 20 year period at 11.25% interest compounded monthly is

R = Pi/[1 - (1 +i)^(-n)] where P = 60,000, i = .1125/12 = .009375)(interest compounded monthly, the same period of time as payments are made) and n = 20(12) = 240

R = 60,000(.009375[1 - (1.009375)^(-240))] = $502.59.

TchrWill said:

Ms. Halliday received a mortgage loan from the Bank of Nova Scotia for $60,000 at 11.25% compounded semi-annually for a five-year term. Monthly payments were based on a 20 year amortization period

R = 60,000(.009375[1 - (1.009375)^(-240))] = $502.59.

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TchrWill, that should be 60,000(.009375) / [1 - (1.009375)^(-240)] = $629.55
You musta been tired, because your formula R = Pi / [1 - (1 + i)^(-n)] is correct!

However, 629.55 is still not correct, since the interest is quoted as 11.25% cpd semi-annually,
so must be converted to "cpd monthly" (see TKHunny's post).
11.25 cpd semi-annually = 11.5664..... cpd annually
10.99504... cpd monthly = 11.5664..... cpd annually

So the "i" = .1099504 / 12, which results in a payment of 619.11

So I'm borrowing $60,000 from TK :wink:

Denis wrote:
However, 629.55 is still not correct, since the interest is quoted as 11.25% cpd semi-annually,
so must be converted to "cpd monthly" (see TKHunny's post).
11.25 cpd semi-annually = 11.5664..... cpd annually
10.99504... cpd monthly = 11.5664..... cpd annually

So the "i" = .1099504 / 12, which results in a payment of 619.11

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okay I see how you got the final results but in between the part when we need to convert it . I still seem to be confused. HOw did you get an answer of 11.5664 and the 10.99504. ANd yes I did look at Tk Hunnie notes;

missl said:

okay I see how you got the final results but in between the part when we need to convert it . I still seem to be confused. HOw did you get an answer of 11.5664 and the 10.99504. ANd yes I did look at Tk Hunnie notes;

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These are known as "equivalent rates"; too difficult to teach here;
please start using google to find sites that already explain such stuff; like:
http://in.answers.yahoo.com/question/in ... 440AAjWOjZ

Hi, I know some part I didn;t do it right. Can someone tell me If i miss something

The bank is agreeable to renewing the mortgage for another five-year term at 10% compounded semi-annually. Calculate the size of the monthly payment for the new term of the mortgage.


60,000 (0.050) / [ 1 – (1.050) ^ (-240) ] = 3000 / 0.999992 = 3000

WHEN is this taking place? 5 years after the original mortgage? 10 years?
Regardless, the Amount surely won't be 60,000 !
If it's 5 years later, then you need what's owing THEN.

Nevermind you're right its after 5 year ... So which I got was 55,468.48 and you please just do the rate conversation for me to see ?


55,468.48(? ) / [ 1 – (?) ^ (-240) ] =

missl said:

Nevermind you're right its after 5 year ... So which I got was 55,468.48 and you please just do the rate conversation for me to see ?
55,468.48(? ) / [ 1 – (?) ^ (-240) ] =

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55,468.48 is not correct: you're using i = .1125 / 12 ; you were told to use i = .1099504 / 12
240 is also not correct: 15 years left means 15*12 = 180

You definitely need a face-to-face teacher.
Anyway, to convert 10% cpd. semi-annual to its equivalent cpd. monthly:

Step#1: (1 + .10/2)^2 = (1.05)^2 = 1.1025 : that means that 10.25% is the effective annual rate

Step#2: (1.1025)^(1/12) = 1.0081648..... : so i = .0081648

can I email you what I did??

missl said:

can I email you what I did??

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