Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10764

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10764 – $6900 = $3864

Thus, Simple Interest = $3864

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3864}/_{6900 × 7}

= ³⁸⁶⁴⁰⁰/₄₈₃₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3864 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 7% of Principal

= 7% of $6900

= ⁷/₁₀₀ × 6900

= ^{7 × 6900}/₁₀₀

= ⁴⁸³⁰⁰/₁₀₀ = 483

Thus, simple Interest for 1 year = $483

Now,

∵ If the simple Interest is $483, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₃ years

∴ If the simple Interest is $3864, then the time = ¹/₄₈₃ × 3864 years

= ^{1 × 3864}/₄₈₃ years

= ³⁸⁶⁴/₄₈₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.

(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.