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) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(3) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(5) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.