Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
Correct Answer
$8320
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 6% × 10
= $5200 ×6/100 × 10
= 5200 × 6 × 10/100
= 31200 × 10/100
= 312000/100
= $3120
Thus, Simple Interest = $3120
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 = $5200 + $3120
= $8320
Thus, Amount to be paid = $8320 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 = $5200
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 6% × 10)
= $5200 + ($5200 ×6/100 × 10)
= $5200 + (5200 × 6 × 10/100)
= $5200 + (31200 × 10/100)
= $5200 + (312000/100)
= $5200 + $3120 = $8320
Thus, Amount (A) to be paid = $8320 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 $5200, the simple interest in 1 year
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $312 × 10 = $3120
Thus, Simple Interest (SI) = $3120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3120
= $8320
Thus, Amount to be paid = $8320 Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.