Question:
Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
Correct Answer
$8112
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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) = $5200 × 7% × 8
= $5200 ×7/100 × 8
= 5200 × 7 × 8/100
= 36400 × 8/100
= 291200/100
= $2912
Thus, Simple Interest = $2912
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 = $5200 + $2912
= $8112
Thus, Amount to be paid = $8112 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 = $5200
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 7% × 8)
= $5200 + ($5200 ×7/100 × 8)
= $5200 + (5200 × 7 × 8/100)
= $5200 + (36400 × 8/100)
= $5200 + (291200/100)
= $5200 + $2912 = $8112
Thus, Amount (A) to be paid = $8112 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 $5200, the simple interest in 1 year
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = $364
Thus, simple interest for 1 year = $364
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $364 × 8 = $2912
Thus, Simple Interest (SI) = $2912
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2912
= $8112
Thus, Amount to be paid = $8112 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(3) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(6) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(8) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(10) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.