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) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(4) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.