Question:
Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
Correct Answer
$8162
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 6% × 9
= $5300 ×6/100 × 9
= 5300 × 6 × 9/100
= 31800 × 9/100
= 286200/100
= $2862
Thus, Simple Interest = $2862
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 = $5300 + $2862
= $8162
Thus, Amount to be paid = $8162 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 = $5300
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5300 + ($5300 × 6% × 9)
= $5300 + ($5300 ×6/100 × 9)
= $5300 + (5300 × 6 × 9/100)
= $5300 + (31800 × 9/100)
= $5300 + (286200/100)
= $5300 + $2862 = $8162
Thus, Amount (A) to be paid = $8162 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 $5300, the simple interest in 1 year
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = $318
Thus, simple interest for 1 year = $318
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $318 × 9 = $2862
Thus, Simple Interest (SI) = $2862
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2862
= $8162
Thus, Amount to be paid = $8162 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(2) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(3) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?