Question:
Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.
Correct Answer
$4864
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 7%
Time (t) = 4 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) = $3800 × 7% × 4
= $3800 ×7/100 × 4
= 3800 × 7 × 4/100
= 26600 × 4/100
= 106400/100
= $1064
Thus, Simple Interest = $1064
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 = $3800 + $1064
= $4864
Thus, Amount to be paid = $4864 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 = $3800
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3800 + ($3800 × 7% × 4)
= $3800 + ($3800 ×7/100 × 4)
= $3800 + (3800 × 7 × 4/100)
= $3800 + (26600 × 4/100)
= $3800 + (106400/100)
= $3800 + $1064 = $4864
Thus, Amount (A) to be paid = $4864 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 $3800, the simple interest in 1 year
= 7/100 × 3800
= 7 × 3800/100
= 26600/100 = $266
Thus, simple interest for 1 year = $266
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $266 × 4 = $1064
Thus, Simple Interest (SI) = $1064
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $1064
= $4864
Thus, Amount to be paid = $4864 Answer
Similar Questions
(1) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(8) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(10) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.