Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6497.5

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

$6497.5 = P (1 + 3% × 5)

⇒ $6497.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6497.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6497.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6497.5 = P (^{100 + 15}/₁₀₀)

⇒ $6497.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6497.5

⇒ P = ^6497.5/_¹¹⁵/100

⇒ P = 6497.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6497.5 × 100}/₁₁₅

⇒ P = ⁶⁴⁹⁷⁵⁰/₁₁₅

⇒ 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 = 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 6497.5, then the Principal = ¹⁰⁰/₁₁₅ × 6497.5

= ^{100 × 6497.5}/₁₁₅

= ⁶⁴⁹⁷⁵⁰/₁₁₅

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(4) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(6) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(7) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?

(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.