Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
Correct Answer
$8778
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 6% × 9
= $5700 ×6/100 × 9
= 5700 × 6 × 9/100
= 34200 × 9/100
= 307800/100
= $3078
Thus, Simple Interest = $3078
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 = $5700 + $3078
= $8778
Thus, Amount to be paid = $8778 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 = $5700
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 6% × 9)
= $5700 + ($5700 ×6/100 × 9)
= $5700 + (5700 × 6 × 9/100)
= $5700 + (34200 × 9/100)
= $5700 + (307800/100)
= $5700 + $3078 = $8778
Thus, Amount (A) to be paid = $8778 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 $5700, the simple interest in 1 year
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = $342
Thus, simple interest for 1 year = $342
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $342 × 9 = $3078
Thus, Simple Interest (SI) = $3078
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3078
= $8778
Thus, Amount to be paid = $8778 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(10) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.