Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
Correct Answer
$7680
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $6000 ×4/100 × 7
= 6000 × 4 × 7/100
= 24000 × 7/100
= 168000/100
= $1680
Thus, Simple Interest = $1680
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 + $1680
= $7680
Thus, Amount to be paid = $7680 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $6000 + ($6000 × 4% × 7)
= $6000 + ($6000 ×4/100 × 7)
= $6000 + (6000 × 4 × 7/100)
= $6000 + (24000 × 7/100)
= $6000 + (168000/100)
= $6000 + $1680 = $7680
Thus, Amount (A) to be paid = $7680 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $6000, the simple interest in 1 year
= 4/100 × 6000
= 4 × 6000/100
= 24000/100 = $240
Thus, simple interest for 1 year = $240
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $240 × 7 = $1680
Thus, Simple Interest (SI) = $1680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $1680
= $7680
Thus, Amount to be paid = $7680 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(4) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(6) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(7) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 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 10% simple interest?