Question

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?

Answer 1

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 ) .

Answer 2

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

Answer 3

@IrishBoy123

Answer 4

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..

Answer 5

i can help you with this

time is the issue

will try logging on a bit later, if you are online

Answer 6

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.

Answer 7

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