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) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.
(3) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(7) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.