Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $8084

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 = $8084 – $4700 = $3384

Thus, Simple Interest = $3384

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 × 3384}/_{4700 × 8}

= ³³⁸⁴⁰⁰/₃₇₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4700

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

Simple Interest = $3384 (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 $4700

= ⁸/₁₀₀ × 4700

= ^{8 × 4700}/₁₀₀

= ³⁷⁶⁰⁰/₁₀₀ = 376

Thus, simple Interest for 1 year = $376

Now,

∵ If the simple Interest is $376, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₆ years

∴ If the simple Interest is $3384, then the time = ¹/₃₇₆ × 3384 years

= ^{1 × 3384}/₃₇₆ years

= ³³⁸⁴/₃₇₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(2) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(5) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.

(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.