Question:
What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
Correct Answer
$6160
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3850 × 10% × 6
= $3850 ×10/100 × 6
= 3850 × 10 × 6/100
= 38500 × 6/100
= 231000/100
= $2310
Thus, Simple Interest = $2310
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 = $3850 + $2310
= $6160
Thus, Amount to be paid = $6160 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 = $3850
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3850 + ($3850 × 10% × 6)
= $3850 + ($3850 ×10/100 × 6)
= $3850 + (3850 × 10 × 6/100)
= $3850 + (38500 × 6/100)
= $3850 + (231000/100)
= $3850 + $2310 = $6160
Thus, Amount (A) to be paid = $6160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3850, the simple interest in 1 year
= 10/100 × 3850
= 10 × 3850/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $385 × 6 = $2310
Thus, Simple Interest (SI) = $2310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $2310
= $6160
Thus, Amount to be paid = $6160 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?