Question:
What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
Correct Answer
$5265
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 7%
Time (t) = 5 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) = $3900 × 7% × 5
= $3900 ×7/100 × 5
= 3900 × 7 × 5/100
= 27300 × 5/100
= 136500/100
= $1365
Thus, Simple Interest = $1365
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 = $3900 + $1365
= $5265
Thus, Amount to be paid = $5265 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 = $3900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 5 years
Thus, Amount (A)
= $3900 + ($3900 × 7% × 5)
= $3900 + ($3900 ×7/100 × 5)
= $3900 + (3900 × 7 × 5/100)
= $3900 + (27300 × 5/100)
= $3900 + (136500/100)
= $3900 + $1365 = $5265
Thus, Amount (A) to be paid = $5265 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 $3900, the simple interest in 1 year
= 7/100 × 3900
= 7 × 3900/100
= 27300/100 = $273
Thus, simple interest for 1 year = $273
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $273 × 5 = $1365
Thus, Simple Interest (SI) = $1365
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1365
= $5265
Thus, Amount to be paid = $5265 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(3) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(5) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(7) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.