Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6970

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 = $6970 – $4100 = $2870

Thus, Simple Interest = $2870

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 × 2870}/_{4100 × 7}

= ²⁸⁷⁰⁰⁰/₂₈₇₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 7% per annum

Simple Interest = $2870 (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 $4100

= ⁷/₁₀₀ × 4100

= ^{7 × 4100}/₁₀₀

= ²⁸⁷⁰⁰/₁₀₀ = 287

Thus, simple Interest for 1 year = $287

Now,

∵ If the simple Interest is $287, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₇ years

∴ If the simple Interest is $2870, then the time = ¹/₂₈₇ × 2870 years

= ^{1 × 2870}/₂₈₇ years

= ²⁸⁷⁰/₂₈₇ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

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

(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(8) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.