Question:
Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
Correct Answer
$6448
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5200 ×3/100 × 8
= 5200 × 3 × 8/100
= 15600 × 8/100
= 124800/100
= $1248
Thus, Simple Interest = $1248
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 + $1248
= $6448
Thus, Amount to be paid = $6448 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 3% × 8)
= $5200 + ($5200 ×3/100 × 8)
= $5200 + (5200 × 3 × 8/100)
= $5200 + (15600 × 8/100)
= $5200 + (124800/100)
= $5200 + $1248 = $6448
Thus, Amount (A) to be paid = $6448 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5200, the simple interest in 1 year
= 3/100 × 5200
= 3 × 5200/100
= 15600/100 = $156
Thus, simple interest for 1 year = $156
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $156 × 8 = $1248
Thus, Simple Interest (SI) = $1248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1248
= $6448
Thus, Amount to be paid = $6448 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(2) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(7) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.