Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6724

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 = $6724 – $4100 = $2624

Thus, Simple Interest = $2624

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 × 2624}/_{4100 × 8}

= ²⁶²⁴⁰⁰/₃₂₈₀₀

= 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) = $4100

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

Simple Interest = $2624 (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 $4100

= ⁸/₁₀₀ × 4100

= ^{8 × 4100}/₁₀₀

= ³²⁸⁰⁰/₁₀₀ = 328

Thus, simple Interest for 1 year = $328

Now,

∵ If the simple Interest is $328, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₈ years

∴ If the simple Interest is $2624, then the time = ¹/₃₂₈ × 2624 years

= ^{1 × 2624}/₃₂₈ years

= ²⁶²⁴/₃₂₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(4) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(6) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.

(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.