Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
Correct Answer
$8239
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5350 × 6% × 9
= $5350 ×6/100 × 9
= 5350 × 6 × 9/100
= 32100 × 9/100
= 288900/100
= $2889
Thus, Simple Interest = $2889
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2889
= $8239
Thus, Amount to be paid = $8239 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5350
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 6% × 9)
= $5350 + ($5350 ×6/100 × 9)
= $5350 + (5350 × 6 × 9/100)
= $5350 + (32100 × 9/100)
= $5350 + (288900/100)
= $5350 + $2889 = $8239
Thus, Amount (A) to be paid = $8239 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5350, the simple interest in 1 year
= 6/100 × 5350
= 6 × 5350/100
= 32100/100 = $321
Thus, simple interest for 1 year = $321
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $321 × 9 = $2889
Thus, Simple Interest (SI) = $2889
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2889
= $8239
Thus, Amount to be paid = $8239 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(2) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
(4) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(9) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?