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) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.

(3) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.