Question:
Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
Correct Answer
$5148
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 8%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3900 × 8% × 4
= $3900 ×8/100 × 4
= 3900 × 8 × 4/100
= 31200 × 4/100
= 124800/100
= $1248
Thus, Simple Interest = $1248
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 = $3900 + $1248
= $5148
Thus, Amount to be paid = $5148 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 = $3900
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3900 + ($3900 × 8% × 4)
= $3900 + ($3900 ×8/100 × 4)
= $3900 + (3900 × 8 × 4/100)
= $3900 + (31200 × 4/100)
= $3900 + (124800/100)
= $3900 + $1248 = $5148
Thus, Amount (A) to be paid = $5148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3900, the simple interest in 1 year
= 8/100 × 3900
= 8 × 3900/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $312 × 4 = $1248
Thus, Simple Interest (SI) = $1248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $1248
= $5148
Thus, Amount to be paid = $5148 Answer
Similar Questions
(1) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(3) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.