Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
Correct Answer
$9360
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $6000 × 7% × 8
= $6000 ×7/100 × 8
= 6000 × 7 × 8/100
= 42000 × 8/100
= 336000/100
= $3360
Thus, Simple Interest = $3360
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 = $6000 + $3360
= $9360
Thus, Amount to be paid = $9360 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 = $6000
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 7% × 8)
= $6000 + ($6000 ×7/100 × 8)
= $6000 + (6000 × 7 × 8/100)
= $6000 + (42000 × 8/100)
= $6000 + (336000/100)
= $6000 + $3360 = $9360
Thus, Amount (A) to be paid = $9360 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $6000, the simple interest in 1 year
= 7/100 × 6000
= 7 × 6000/100
= 42000/100 = $420
Thus, simple interest for 1 year = $420
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $420 × 8 = $3360
Thus, Simple Interest (SI) = $3360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3360
= $9360
Thus, Amount to be paid = $9360 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(2) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(10) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.