Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
Correct Answer
$8670
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5100 ×7/100 × 10
= 5100 × 7 × 10/100
= 35700 × 10/100
= 357000/100
= $3570
Thus, Simple Interest = $3570
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 + $3570
= $8670
Thus, Amount to be paid = $8670 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 7% × 10)
= $5100 + ($5100 ×7/100 × 10)
= $5100 + (5100 × 7 × 10/100)
= $5100 + (35700 × 10/100)
= $5100 + (357000/100)
= $5100 + $3570 = $8670
Thus, Amount (A) to be paid = $8670 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5100, the simple interest in 1 year
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $357 × 10 = $3570
Thus, Simple Interest (SI) = $3570
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3570
= $8670
Thus, Amount to be paid = $8670 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.