Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
Correct Answer
$5254
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 7%
Time (t) = 6 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) = $3700 × 7% × 6
= $3700 ×7/100 × 6
= 3700 × 7 × 6/100
= 25900 × 6/100
= 155400/100
= $1554
Thus, Simple Interest = $1554
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 = $3700 + $1554
= $5254
Thus, Amount to be paid = $5254 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 = $3700
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 7% × 6)
= $3700 + ($3700 ×7/100 × 6)
= $3700 + (3700 × 7 × 6/100)
= $3700 + (25900 × 6/100)
= $3700 + (155400/100)
= $3700 + $1554 = $5254
Thus, Amount (A) to be paid = $5254 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 $3700, the simple interest in 1 year
= 7/100 × 3700
= 7 × 3700/100
= 25900/100 = $259
Thus, simple interest for 1 year = $259
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $259 × 6 = $1554
Thus, Simple Interest (SI) = $1554
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1554
= $5254
Thus, Amount to be paid = $5254 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.