Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $7820

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

$7820 = P (1 + 3% × 5)

⇒ $7820 = P (1 + ³/₁₀₀ × 5)

⇒ $7820 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7820 = P (1 + ¹⁵/₁₀₀)

⇒ $7820 = P (^{100 + 15}/₁₀₀)

⇒ $7820 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7820

⇒ P = ⁷⁸²⁰/_¹¹⁵/100

⇒ P = 7820 × ¹⁰⁰/₁₁₅

⇒ P = ^{7820 × 100}/₁₁₅

⇒ P = ⁷⁸²⁰⁰⁰/₁₁₅

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 7820, then the Principal = ¹⁰⁰/₁₁₅ × 7820

= ^{100 × 7820}/₁₁₅

= ⁷⁸²⁰⁰⁰/₁₁₅

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?