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) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?