Simple Interest
Math MCQs

Question :    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.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6720

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 = $6720 – $4200 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{4200 × 6}

= ²⁵²⁰⁰⁰/₂₅₂₀₀

= 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) = $4200

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2520 (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 = 6% of Principal

= 6% of $4200

= ⁶/₁₀₀ × 4200

= ^{6 × 4200}/₁₀₀

= ²⁵²⁰⁰/₁₀₀ = 252

Thus, simple Interest for 1 year = $252

Now,

∵ If the simple Interest is $252, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₂ years

∴ If the simple Interest is $2520, then the time = ¹/₂₅₂ × 2520 years

= ^{1 × 2520}/₂₅₂ years

= ²⁵²⁰/₂₅₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(3) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(4) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.

(6) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.

(9) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.