Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6215

Rate of Simple Interest (R) = 2%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$6215 = P (1 + 2% × 5)

⇒ $6215 = P (1 + ²/₁₀₀ × 5)

⇒ $6215 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6215 = P (1 + ¹⁰/₁₀₀)

⇒ $6215 = P (^{100 + 10}/₁₀₀)

⇒ $6215 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6215

⇒ P = ⁶²¹⁵/_¹¹⁰/100

⇒ P = 6215 × ¹⁰⁰/₁₁₀

⇒ P = ^{6215 × 100}/₁₁₀

⇒ P = ⁶²¹⁵⁰⁰/₁₁₀

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6215, then the Principal = ¹⁰⁰/₁₁₀ × 6215

= ^{100 × 6215}/₁₁₀

= ⁶²¹⁵⁰⁰/₁₁₀

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.

(2) 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.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(5) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.

(8) 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.

(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?