Simple Interest
Math MCQs

Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?

Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $7187.5

Rate of Simple Interest (R) = 3%

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

$7187.5 = P (1 + 3% × 5)

⇒ $7187.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7187.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7187.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7187.5 = P (^{100 + 15}/₁₀₀)

⇒ $7187.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7187.5

⇒ P = ^7187.5/_¹¹⁵/100

⇒ P = 7187.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7187.5 × 100}/₁₁₅

⇒ P = ⁷¹⁸⁷⁵⁰/₁₁₅

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7187.5, then the Principal = ¹⁰⁰/₁₁₅ × 7187.5

= ^{100 × 7187.5}/₁₁₅

= ⁷¹⁸⁷⁵⁰/₁₁₅

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer

Similar Questions

(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?

(2) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

(5) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?

(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(9) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.