Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
Correct Answer
$7260
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $6000 ×3/100 × 7
= 6000 × 3 × 7/100
= 18000 × 7/100
= 126000/100
= $1260
Thus, Simple Interest = $1260
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 + $1260
= $7260
Thus, Amount to be paid = $7260 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $6000 + ($6000 × 3% × 7)
= $6000 + ($6000 ×3/100 × 7)
= $6000 + (6000 × 3 × 7/100)
= $6000 + (18000 × 7/100)
= $6000 + (126000/100)
= $6000 + $1260 = $7260
Thus, Amount (A) to be paid = $7260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $6000, the simple interest in 1 year
= 3/100 × 6000
= 3 × 6000/100
= 18000/100 = $180
Thus, simple interest for 1 year = $180
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $180 × 7 = $1260
Thus, Simple Interest (SI) = $1260
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1260
= $7260
Thus, Amount to be paid = $7260 Answer
Similar Questions
(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
(2) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(5) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?