Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
Correct Answer
$6565
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 3% × 10
= $5050 ×3/100 × 10
= 5050 × 3 × 10/100
= 15150 × 10/100
= 151500/100
= $1515
Thus, Simple Interest = $1515
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 = $5050 + $1515
= $6565
Thus, Amount to be paid = $6565 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 = $5050
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 3% × 10)
= $5050 + ($5050 ×3/100 × 10)
= $5050 + (5050 × 3 × 10/100)
= $5050 + (15150 × 10/100)
= $5050 + (151500/100)
= $5050 + $1515 = $6565
Thus, Amount (A) to be paid = $6565 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 $5050, the simple interest in 1 year
= 3/100 × 5050
= 3 × 5050/100
= 15150/100 = $151.5
Thus, simple interest for 1 year = $151.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $151.5 × 10 = $1515
Thus, Simple Interest (SI) = $1515
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1515
= $6565
Thus, Amount to be paid = $6565 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.