Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8692

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 = $8692 – $5300 = $3392

Thus, Simple Interest = $3392

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 × 3392}/_{5300 × 8}

= ³³⁹²⁰⁰/₄₂₄₀₀

= 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) = $5300

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3392 (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 = 8% of Principal

= 8% of $5300

= ⁸/₁₀₀ × 5300

= ^{8 × 5300}/₁₀₀

= ⁴²⁴⁰⁰/₁₀₀ = 424

Thus, simple Interest for 1 year = $424

Now,

∵ If the simple Interest is $424, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₄ years

∴ If the simple Interest is $3392, then the time = ¹/₄₂₄ × 3392 years

= ^{1 × 3392}/₄₂₄ years

= ³³⁹²/₄₂₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?

(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(5) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.

(9) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.