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) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(3) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.

(7) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.

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