Financial Maths Urgent Help! (1 Viewer)

[Blazerkidd]

Couple of these Q's below I've been stuck on for some time :S... financial maths is so hard! I think this stuff is related to annuities/loan repayments - textbook btw is 'Insight' by John Ley/Michael Fuller

1. Calculate the effective interest rate for this loan using simple interest: $550 over 2 years at 13% p.a. flat interest with repayments 6 monthly

2. Calculate the effective interest rate for this loan using simple interest: $3000 over 4 years at 17% p.a. flat interest with repayments monthly

3. Paul and Pat take out a loan of $90000 over 20 years at 8.25% p.a. interest compounding monthly. Their repayment is $767 per month. After 3 years of repaying the loan Paul wins $20000. They pay this amount off their loan.

a. How long will it take to repay the loan?

b. Calculate the total amount that would have been paid without the lump sum

c. How much is saved by making the lump sum payment?

(a, b and c are with Q3)

If anybody could solve these with worked solutions using Gen Maths methods, would be greatly appreciated


P.S. Tried posting this in the 'Gen Maths' forum mods but unfortunately no reply :l - hopefully ppl doing 3U/4U will be able to solve them!

 

[deswa1]

I did it but I don't think what I did was General level. Are these problems meant to involve sums of geometric sequences and logs? If you want, I can take a photo of my solution but its quite complicated...

 

[Blazerkidd]

I did it but I don't think what I did was General level. Are these problems meant to involve sums of geometric sequences and logs? If you want, I can take a photo of my solution but its quite complicated...

yeah absolutely - i've been toiling at these Qs for god knows how long... well from what the textbook suggests - you have to use the formula for effective interest rate E = (1+r)^n - 1 for Q1/2 and annuities for Q3.

Annuities formulas :
Present: N = M[(1+r)^n - 1]/r(1+r)^n where M = contribution paid at end of each period, r = compound rate, n = no. of time periods
Future: A = M[(1+r)^n - 1]/r where M = ...

Well, if you could post it up, that'd be great dude - i'll just try to understand 2U Maths haha. Could you possibly use info I gave above to solve them?

 

[deswa1]

I don't memorise that formula, but I'll show you a way to easily obtain it, to make the solution easier. I won't solve the whole thing for you, just the layout so you can try it and then learn it much more effectively (BTW, I'm really tired so there's a good chance I made a typo/wrong number/mistake somewhere. If something doesn't make sense, tell me and I'll try and clarify/fix it ) - This is Q3:

1. After month 1 (M1), he will owe 90000(1+8.25%/12) -767
2. After month 2 (M2), he will owe 90000(1+8.25%/12)^2 -767((1+8.25%/12)-767
3. Generalize to after month n (Mn), he will owe owe 90000(1+8.25%/12)^n -767(1+8.25%/12)^n-1-767(1+8.25%/12)^n-2...-767
4. Sum the G.P to work out how much he owes after Month n.
5. After 3 years, (36 months), he pays back $20,000. Work out how much he owes at this point and then subtract $20,000
6. Solve for the remaining months and that's how much time it takes.
7. Part B- Without the lump sum, just solve the G.P obtained in 4 to work out how many months it takes and then multiply by $767 (the amount he pays at each month).
8. Part C- We worked out how many months it took with the lump sum. Use this to work how much he repaid and then subtract this from the result obtained in 7.