Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $6468

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 = $6468 – $4200 = $2268

Thus, Simple Interest = $2268

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 × 2268}/_{4200 × 9}

= ²²⁶⁸⁰⁰/₃₇₈₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 9% per annum

Simple Interest = $2268 (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 = 9% of Principal

= 9% of $4200

= ⁹/₁₀₀ × 4200

= ^{9 × 4200}/₁₀₀

= ³⁷⁸⁰⁰/₁₀₀ = 378

Thus, simple Interest for 1 year = $378

Now,

∵ If the simple Interest is $378, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₈ years

∴ If the simple Interest is $2268, then the time = ¹/₃₇₈ × 2268 years

= ^{1 × 2268}/₃₇₈ years

= ²²⁶⁸/₃₇₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

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

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(3) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(5) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.

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

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.