Simple Interest
Math MCQs

Question :    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?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $9687.5

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

$9687.5 = P (1 + 5% × 5)

⇒ $9687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9687.5 = P (1 + ²⁵/₁₀₀)

⇒ $9687.5 = P (^{100 + 25}/₁₀₀)

⇒ $9687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9687.5

⇒ P = ^9687.5/_¹²⁵/100

⇒ P = 9687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9687.5 × 100}/₁₂₅

⇒ P = ⁹⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 9687.5, then the Principal = ¹⁰⁰/₁₂₅ × 9687.5

= ^{100 × 9687.5}/₁₂₅

= ⁹⁶⁸⁷⁵⁰/₁₂₅

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(5) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.