Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.
Correct Answer
$8418.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5650 × 7% × 7
= $5650 ×7/100 × 7
= 5650 × 7 × 7/100
= 39550 × 7/100
= 276850/100
= $2768.5
Thus, Simple Interest = $2768.5
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 = $5650 + $2768.5
= $8418.5
Thus, Amount to be paid = $8418.5 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 = $5650
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 7% × 7)
= $5650 + ($5650 ×7/100 × 7)
= $5650 + (5650 × 7 × 7/100)
= $5650 + (39550 × 7/100)
= $5650 + (276850/100)
= $5650 + $2768.5 = $8418.5
Thus, Amount (A) to be paid = $8418.5 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 $5650, the simple interest in 1 year
= 7/100 × 5650
= 7 × 5650/100
= 39550/100 = $395.5
Thus, simple interest for 1 year = $395.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $395.5 × 7 = $2768.5
Thus, Simple Interest (SI) = $2768.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2768.5
= $8418.5
Thus, Amount to be paid = $8418.5 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(2) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(7) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.