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) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(6) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(8) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(10) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?