Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $11524

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 = $11524 – $6700 = $4824

Thus, Simple Interest = $4824

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 × 4824}/_{6700 × 9}

= ⁴⁸²⁴⁰⁰/₆₀₃₀₀

= 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) = $6700

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

Simple Interest = $4824 (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 $6700

= ⁹/₁₀₀ × 6700

= ^{9 × 6700}/₁₀₀

= ⁶⁰³⁰⁰/₁₀₀ = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₃ years

∴ If the simple Interest is $4824, then the time = ¹/₆₀₃ × 4824 years

= ^{1 × 4824}/₆₀₃ years

= ⁴⁸²⁴/₆₀₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(3) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?

(4) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.

(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?