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) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(9) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.