Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
Correct Answer
$9520
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5950 × 6% × 10
= $5950 ×6/100 × 10
= 5950 × 6 × 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 = $5950 + $3570
= $9520
Thus, Amount to be paid = $9520 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 = $5950
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 6% × 10)
= $5950 + ($5950 ×6/100 × 10)
= $5950 + (5950 × 6 × 10/100)
= $5950 + (35700 × 10/100)
= $5950 + (357000/100)
= $5950 + $3570 = $9520
Thus, Amount (A) to be paid = $9520 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5950, the simple interest in 1 year
= 6/100 × 5950
= 6 × 5950/100
= 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 = $5950 + $3570
= $9520
Thus, Amount to be paid = $9520 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(2) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(6) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(10) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.