Finance Question? (1 Viewer)

[haz_it_all]

hey i got a question i cant figure out

A man borrows $2million from a bank that charges 5%pa. Semi-annually repayments are made for 5years. After the 5years,the repayment method switches to 6%pa quartly repayments for the next 10 years(where the loan will be fully amortised)

What is the payment amount
i) during the 5year period
ii)during the 10year period


Ive got no idea how to go about solving it so annny help wuld be useful.

Thanks

 

[Grizzly]

So there are 10 repayments at 0.05
then, 20 repayments at 0.06
I;ll use the present value of annuities. Ra ( i , 0.05 ) and Ra ( i , 0.05 ) functions.

2,000,000 = R ( 1 - 1.05^-10 / 0.05 ) + R ( 1 - 1.06^-20 / 0.05 ) ( 1.05)^-10

Thats of the top of my head

Edit:
Oh, solve for "R", the value of the repayments.

 

[jlh]

uh you forgot to adjust the interest rate grizzly...

0.05 is semi annually so j2 = 0.025
and 0.06 is quarterly so j4 = 0.015

 

[jlh]

oh and consequently the time periods..

 

[jlh]

uh..
for i) i think it is:
2000000(1.025)^10 = R ((1.025^10-1)/(0.025)) + R ((1-1.015^-40)/(0.015))(1.015)

 

[Grizzly]

Yeah sorry, i did it in a mega rush.
JLH's way should be right

 

[haz_it_all]

hey thanks!

but can u just explain it to me in words wat ur doing? that wuld be great

 

[jlh]

i:
2000000(1.025)^10 = R ((1.025^10-1)/(0.025)) + R ((1-1.015^-40)/(0.015))(1.015)

first of all you have to convert the interest rate to whatever it states it is in the question, ie. semi- annually 5%pa repayments, so thats just 0.05/2. you also have to adjust the number of time periods or repayments. there would be 10 repayments during the 5 years.

then you gotta pick a focal date, as stated in the question, the 5th year is best because its easiest. you can pick any focal date as long as you do the necessary adjustments.

since i picked the 5th year, you have to adjust the 2mil balance by bringing it forward to that time period using the interest rate. here i used the compound interest formula, 2000000 (1 + i)^n = 2000000 (1.025)^10.

next you'd have to work out the value of each repayment, R, at both interest rates and their time periods. i used both the Ra and Rs formula. the Rs formula calculates the value R at the time of the last repayment, which is at time period 10 in this case (ie. fifth year). the Rs formula corresponds to the R ((1.025^10-1)/(0.025)) part of the equation.

the Ra formula calculates R at the time period before the first repayment. here it would take us back to the 4.75 year. since we want it at the fifth year, we have to bring that amount forward 1 time period or 1 quarter, hence the compound interest. R ((1-1.015^-40)/(0.015))(1.015) corresponds to the Ra formula.


oh i forgot to add, then you calculate the above, and solve for 4, you gotta multiply R by 10. R was just the value of the repayment not the entire repayment amount for that period.

 

[jlh]

uh just wondering, what class is this for and at what uni?