Question:
What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
Correct Answer
$4160
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 5%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3200 × 5% × 6
= $3200 ×5/100 × 6
= 3200 × 5 × 6/100
= 16000 × 6/100
= 96000/100
= $960
Thus, Simple Interest = $960
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 = $3200 + $960
= $4160
Thus, Amount to be paid = $4160 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 = $3200
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3200 + ($3200 × 5% × 6)
= $3200 + ($3200 ×5/100 × 6)
= $3200 + (3200 × 5 × 6/100)
= $3200 + (16000 × 6/100)
= $3200 + (96000/100)
= $3200 + $960 = $4160
Thus, Amount (A) to be paid = $4160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3200, the simple interest in 1 year
= 5/100 × 3200
= 5 × 3200/100
= 16000/100 = $160
Thus, simple interest for 1 year = $160
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $160 × 6 = $960
Thus, Simple Interest (SI) = $960
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $960
= $4160
Thus, Amount to be paid = $4160 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?