Easy Maths Question-help Me! (1 Viewer)

[Bimbo]

OK....people said to post my question here...this is really easy and yes i can't do it-i have no textbooks with me at all and cant remember the formula. is it the compound interest one?? i tried doing this question but got some ridiculously high answer that just didnt seem right.
The question is if $200000 was borrowed over 25 years at 7.4% p.a, compounding monthly, what are the monthly repayments (to be paid in equal instalments) and what is the total interest paid over 25 years.

 

[ezzy85]

Originally posted by Bimbo
OK....people said to post my question here...this is really easy and yes i can't do it-i have no textbooks with me at all and cant remember the formula. is it the compound interest one?? i tried doing this question but got some ridiculously high answer that just didnt seem right.
The question is if $200000 was borrowed over 25 years at 7.4% p.a, compounding monthly, what are the monthly repayments (to be paid in equal instalments) and what is the total interest paid over 25 years.

its compounded monthly so the number of terms is 25 X 12 = 300 and interest = [7.4/100]/12 (let r be this number + 1)

First repayment (M = monthly repayments):

A₁ = 200000(r)¹ - M
A₂ = A₁ (r) - M

A₃₀₀ = 200000(r)³⁰⁰ - M(1 + r + r² + ... + r²⁰⁰)

That last part is a GP where a = 1, n=300 and r = r.
Since the amount owing after 300 terms = 0, A₃₀₀ = 0

200000(r)³⁰⁰ = M(1 + r + r² + ... + r²⁰⁰)

you can then find M.
im getting M = $1439.23
is this right?

 

[OLDMAN]

Following might help in this Gen. Maths question.

Present Value (PV)=200,000
Future Value(FV)=200,000*(1+(7.4/12)/100)*300=1,264,758.58 being the monthly-compounding formula FV=PV*(1+r)^n .
Future Value(FV) of Monthly Instalments M, FV = M*((1+(7.4/12)/100)^300-1)/((7.4/12)/100) being the annuity formula FV=M((1+r)^n-1)/r
These two Future Values must equal:
1,264,758.58=M*((1+(7.4/12)/100)^300-1)/((7.4/12)/100)

Solving for M gives $1,465.

From a financial point of view, the Present Value $200,000, the Future Value $1,264,758 (after 25 years) and the Annuity set of 300 monthly installments of $1,465 are all equal if the annual interest rate is 7.4% per annum.

 

[Bimbo]

Hey thanks heaps guys...i'm going to try and work out the probelm myself now that i have the right formulas You've both been a big help!