Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $9500

Rate of Simple Interest (R) = 5%

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

$9500 = P (1 + 5% × 5)

⇒ $9500 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9500 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9500 = P (1 + ²⁵/₁₀₀)

⇒ $9500 = P (^{100 + 25}/₁₀₀)

⇒ $9500 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9500

⇒ P = ⁹⁵⁰⁰/_¹²⁵/100

⇒ P = 9500 × ¹⁰⁰/₁₂₅

⇒ P = ^{9500 × 100}/₁₂₅

⇒ P = ⁹⁵⁰⁰⁰⁰/₁₂₅

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9500, then the Principal = ¹⁰⁰/₁₂₅ × 9500

= ^{100 × 9500}/₁₂₅

= ⁹⁵⁰⁰⁰⁰/₁₂₅

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?

(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(6) 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.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.