Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $8944

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 = $8944 – $5200 = $3744

Thus, Simple Interest = $3744

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 × 3744}/_{5200 × 8}

= ³⁷⁴⁴⁰⁰/₄₁₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5200

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

Simple Interest = $3744 (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 $5200

= ⁸/₁₀₀ × 5200

= ^{8 × 5200}/₁₀₀

= ⁴¹⁶⁰⁰/₁₀₀ = 416

Thus, simple Interest for 1 year = $416

Now,

∵ If the simple Interest is $416, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₆ years

∴ If the simple Interest is $3744, then the time = ¹/₄₁₆ × 3744 years

= ^{1 × 3744}/₄₁₆ years

= ³⁷⁴⁴/₄₁₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

(2) 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.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(5) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) 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.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.