Lillian borrows $10,000. She borrows some from her friend at 8% annual interest, twice as much as that from her bank at 9%, and the remainder from her insurance company at 5%. She pays a total of $830 of interest for the first year. How much did she borrow from the insurance company? a. $3000 c. $6000 b. $1000 d. $2300 Please select the best answer from the choices provided
Answers
Answer:
Option (b)
$ 1000
Step-by-step explanation:
Solution :-
Let the amount Lillian borrowed from her friend be $ X
Rate of Interest on it = 8%
We know that
Simple Interest = PTR/100
Simple Interest for first year
We have,
P = $ X
T = 1 year
R = 8%
=> S.I. = (X×1×8)/100
=> S.I. = 8X/100
=> S.I. = 2X/25
Simple Interest for the first year
= $ 2X/25
The amount borrowed from the bank
= Twice the amount borrowed from her friend
= $ 2X
Rate of interest on it = 9%
We know that
Simple Interest = PTR/100
Simple Interest for first year
We have,
P = $ 2X
T = 1 year
R = 9%
=> S.I. = (2X×1×9)/100
=> S.I. = 18X/100
=> S.I. = 9X/50
Simple Interest for the first year
= $ 9X/50
Total amount borrowed from her friend and the bank = $ X + $ 2X = $ 3X
Total amount Lillian borrowed = $ 10000
Remaining amount = $ (10000-3X)
So, Remaining money she borrowed from insurance company = $ (10000-3X)
Rate of interest on it = 5%
We know that
Simple Interest = PTR/100
Simple Interest for first year
We have,
P = $ (10000-3X)
T = 1 year
R = 5%
=> S.I. = [(10000-3X)×1×5)/100
=> S.I. = (10000-3X)/20
Simple Interest for the first year
= $ (10000-3X)/20
Total simple Interest for the first year
= [2X/25]+ [9X/50]+ [(10000-3X)/20]
LCM of 25 , 50 and 20 = 100
= [8X+18X+5(10000-3X)]/100
= (26X+50000-15X)/100
= (11X+50000)/100
Simple Interest to be paid for the first year by Lillian = $ (11X+50000)/100
According to the given problem
Simple Interest paid by Lillian for the first year= $ 830
Therefore, (11X+50000)/100 = 830
=> 11X +50000 = 830×100
=> 11X + 50000 = 83000
=> 11X = 83000-50000
=> 11X = 33000
=> X = 33000/11
=> X = 3000
Therefore, X = $ 3000
Money borrowed from her friend
= $ 3000
Money borrowed from the bank
= $ 2X
= $ 2×3000
= $ 6000
Money borrowed from the insurance company = $ (10000-3X)
= $ (10000-3×3000)
= $ (10000-9000)
= $ 1000
(or)
Money borrowed from the insurance company
= $ 10000-(3000+6000)
= $ (10000-9000)
= $ 1000
Therefore , money borrowed from the insurance company = $ 1000
Answer:-
Money borrowed from the insurance company by Lillian is $ 1000
Used formulae:-
→ Simple Interest (S.I.) = PTR/100
- P = Principal
- T = Time
- R = Rate of Interest