Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
Correct Answer
$6760
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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% × 10
= $5200 ×3/100 × 10
= 5200 × 3 × 10/100
= 15600 × 10/100
= 156000/100
= $1560
Thus, Simple Interest = $1560
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 + $1560
= $6760
Thus, Amount to be paid = $6760 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) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 3% × 10)
= $5200 + ($5200 ×3/100 × 10)
= $5200 + (5200 × 3 × 10/100)
= $5200 + (15600 × 10/100)
= $5200 + (156000/100)
= $5200 + $1560 = $6760
Thus, Amount (A) to be paid = $6760 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 10 years
= Simple interest for 1 year × 10
= $156 × 10 = $1560
Thus, Simple Interest (SI) = $1560
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1560
= $6760
Thus, Amount to be paid = $6760 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(4) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(8) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.