Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
Correct Answer
$4030
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3100 × 10% × 3
= $3100 ×10/100 × 3
= 3100 × 10 × 3/100
= 31000 × 3/100
= 93000/100
= $930
Thus, Simple Interest = $930
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 = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 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 = $3100
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 10% × 3)
= $3100 + ($3100 ×10/100 × 3)
= $3100 + (3100 × 10 × 3/100)
= $3100 + (31000 × 3/100)
= $3100 + (93000/100)
= $3100 + $930 = $4030
Thus, Amount (A) to be paid = $4030 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3100, the simple interest in 1 year
= 10/100 × 3100
= 10 × 3100/100
= 31000/100 = $310
Thus, simple interest for 1 year = $310
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $310 × 3 = $930
Thus, Simple Interest (SI) = $930
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?