Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
Correct Answer
$6120
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 2% × 10
= $5100 ×2/100 × 10
= 5100 × 2 × 10/100
= 10200 × 10/100
= 102000/100
= $1020
Thus, Simple Interest = $1020
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 = $5100 + $1020
= $6120
Thus, Amount to be paid = $6120 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 = $5100
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 2% × 10)
= $5100 + ($5100 ×2/100 × 10)
= $5100 + (5100 × 2 × 10/100)
= $5100 + (10200 × 10/100)
= $5100 + (102000/100)
= $5100 + $1020 = $6120
Thus, Amount (A) to be paid = $6120 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 $5100, the simple interest in 1 year
= 2/100 × 5100
= 2 × 5100/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $102 × 10 = $1020
Thus, Simple Interest (SI) = $1020
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1020
= $6120
Thus, Amount to be paid = $6120 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(5) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(8) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.