# Calculate the size of the loan payment or deposit.

#### missl

##### New member
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 #### tkhunny ##### Moderator Staff member 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: $$\displaystyle i^{(12)}\;=\;[(1+i^{(2)})^{1/6}]\;-\;1$$ #### missl ##### New member Hi, I just want to make this clearly.. So the interest part is wrong right?? and how did you get the 1/6 part? #### TchrWill ##### Full Member ...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.
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.

#### Denis

##### Senior Member
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.
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:

#### missl

##### New member
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

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;

#### Denis

##### Senior Member
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;
These are known as "equivalent rates"; too difficult to teach here;

#### missl

##### New member
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

#### Denis

##### Senior Member
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.

#### missl

##### New member
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) ] =

#### Denis

##### Senior Member
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) ] =
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

#### missl

##### New member
can I email you what I did??

#### stapel

##### Super Moderator
Staff member
missl said:
can I email you what I did??
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