2 Loan Repay. Qu's (1 Viewer)

[currysauce]

1. A loan of $6000 over 5 years at 15% p.a. interest, is charged monthly, is paid back in 5 yearly installments. How much is each installment, and how much money is paid all together

Tried it too many times, can't get each installments value. ANSWER: $1835.68 ; $9718.40

2. Get Rich Bank offers a mortgage at 13.5% p.a. over 10 years and Capital Bank offers a mortgage at 10% p.a. over 25 years.
i) Find the amount of repayment to each bank on a loan of $80000
ii) Find which total amount paid back will be less

I understand the question, dont get the right answer

ANSWER: I)Get Rich Bank $1218.19 Capital Bank $755.35

II) GRB: $146182.80 ; less than capital bank ($226605.00)

 

[acmilan]

1. A loan of $6000 over 5 years at 15% p.a. interest, is charged monthly, is paid back in 5 yearly installments. How much is each installment, and how much money is paid all together

Let M be the installments

A(1) = 6000 + 6000*(0.0125) = 6000(1 + 0.0125)
A(2) = 6000(1 + 0.0125) + 6000(1 + 0.0125)*(0.0125) = 6000(1 + 0.0125)²
.
.
.
A(12) = 6000(1 + 0.0125)¹¹ + 6000(1 + 0.0125)¹¹(0.0125) - M = 6000(1 + 0.0125)¹² - M

A(13) = (6000(1 + 0.0125)¹² - M) + (6000(1 + 0.0125)¹² - M)(0.0125) = (6000(1 + 0.0125)¹³ - M(1 + 0.0125))
.
.
.
A(60) = 6000(1+0.0125)⁶⁰ - M[(1+0.0125)⁴⁸ + (1+0.0125)³⁶ + (1+0.0125)²⁴ + (1+0.0125)¹² + 1]

A(60) = 0

simplify and you get M = $1835.68

So that M value is payed back once a year for 5 years, so total = 5*1835.68 = $9178.41


Wow that was pretty long

 

[SaHbEeWaH]

i remember this controversial series question
from maths in focus
what the question forgot to tell you was it's meant to be paid back in monthly intervals

in which case (skipping working)
M = 80000(1.01125¹²⁰)/(1.01125¹¹⁹+1.01125¹¹⁸+...+1)

S₁₂₀ = (1.01125¹²⁰ - 1)/0.01125 = 251.41...

M = 80000(1.01125¹²⁰)/251.41...
= $1218.19

and yea you can do the other one now
btw it's meant to be 10.5%p.a. for capital bank

edit: apparently mortgages are always paid monthly. i guess that was meant to be assumed knowledge?. .

 

[currysauce]

thanks guys!!

wohooo finished the whole maths course!!!! 2/3u!