Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
Correct Answer
$4030
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 6%
Time (t) = 5 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) = $3100 × 6% × 5
= $3100 ×6/100 × 5
= 3100 × 6 × 5/100
= 18600 × 5/100
= 93000/100
= $930
Thus, Simple Interest = $930
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 = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 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 = $3100
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 6% × 5)
= $3100 + ($3100 ×6/100 × 5)
= $3100 + (3100 × 6 × 5/100)
= $3100 + (18600 × 5/100)
= $3100 + (93000/100)
= $3100 + $930 = $4030
Thus, Amount (A) to be paid = $4030 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 $3100, the simple interest in 1 year
= 6/100 × 3100
= 6 × 3100/100
= 18600/100 = $186
Thus, simple interest for 1 year = $186
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $186 × 5 = $930
Thus, Simple Interest (SI) = $930
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $930
= $4030
Thus, Amount to be paid = $4030 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.