## anonymous one year ago Charlotte takes a bank loan of 10000\$ . The interest rate is 4 % per annum and repayment period of 5 years. The loan will be paid monthly ie, the number of installments is 60. What will Charlotte's total cost of the loan be if it is a 1 ) the straight-line amortization , ie, the same amount is amortized monthly, 2) installment loans ie the total amount (principal + interest) is paid each month?

1. anonymous

Derive formulas to calculate the total cost of the loan in both cases , as well as annuity ( cost per payment date ) in installment loans , for arbitrary values ​​of the loan amount ( S ) , interest rate ( r) , installment time (T ) and the number of installments ( n ) .

2. anonymous

Im probably is going to use this equation $\sum_{k=0}^{n}x^k=1+x+x^2+x^3+...+x^n=\frac{ x ^{n+1}-1 }{ k-1 }, k \neq 0$

3. anonymous

@IrishBoy123

4. anonymous

from this $\frac{ 100000 }{ 60 }+\frac{ 10000*0.04 }{ 12 }=2000$ I get what she pays to the bank the first month, but only the first 100000/60=1667 she pays to the loan... and that I need somewhere in the equation..

5. IrishBoy123

i can help you with this time is the issue will try logging on a bit later, if you are online

6. IrishBoy123

for straight line amortisation, the principal component of each monthly payment is $$\\dfrac{10,000}{60} = \ 166.\dot6$$ the interest component is the **monthly rate** times the then opening principal balance at the rate of $$4 \% pa$$, which is typically [and wrongly] calculated as $$\dfrac{4 \%}{12} = 0.\dot3 \%$$ per months: 1/ the principal payment for the first period is $$\ 166.\dot6$$, as it is for every period. whereas, 2/ the interest payment is $$\dfrac{4 \%}{12} \cdot \10,000$$ for the next period, the principal payment is $$\ 166.\dot6$$ , as it is for every period. but the interest payment is $$\dfrac{4 \%}{12} \cdot (\10,000- \ 166.\dot6)$$ that pattern repeats itself until the loan is repaid.

7. anonymous

@IrishBoy123 I solved this one in school!! need help with a new one though! thanks!