Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
Correct Answer
$9840
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $6000 ×8/100 × 8
= 6000 × 8 × 8/100
= 48000 × 8/100
= 384000/100
= $3840
Thus, Simple Interest = $3840
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 + $3840
= $9840
Thus, Amount to be paid = $9840 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 8% × 8)
= $6000 + ($6000 ×8/100 × 8)
= $6000 + (6000 × 8 × 8/100)
= $6000 + (48000 × 8/100)
= $6000 + (384000/100)
= $6000 + $3840 = $9840
Thus, Amount (A) to be paid = $9840 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $6000, the simple interest in 1 year
= 8/100 × 6000
= 8 × 6000/100
= 48000/100 = $480
Thus, simple interest for 1 year = $480
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $480 × 8 = $3840
Thus, Simple Interest (SI) = $3840
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3840
= $9840
Thus, Amount to be paid = $9840 Answer
Similar Questions
(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 3% simple interest?
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(3) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(8) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.