Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
Correct Answer
$6060
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5050 ×2/100 × 10
= 5050 × 2 × 10/100
= 10100 × 10/100
= 101000/100
= $1010
Thus, Simple Interest = $1010
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 + $1010
= $6060
Thus, Amount to be paid = $6060 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 10)
= $5050 + ($5050 ×2/100 × 10)
= $5050 + (5050 × 2 × 10/100)
= $5050 + (10100 × 10/100)
= $5050 + (101000/100)
= $5050 + $1010 = $6060
Thus, Amount (A) to be paid = $6060 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5050, the simple interest in 1 year
= 2/100 × 5050
= 2 × 5050/100
= 10100/100 = $101
Thus, simple interest for 1 year = $101
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $101 × 10 = $1010
Thus, Simple Interest (SI) = $1010
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1010
= $6060
Thus, Amount to be paid = $6060 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(5) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(6) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?