Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $9088

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 = $9088 – $6400 = $2688

Thus, Simple Interest = $2688

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 × 2688}/_{6400 × 7}

= ²⁶⁸⁸⁰⁰/₄₄₈₀₀

= 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) = $6400

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

Simple Interest = $2688 (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 $6400

= ⁷/₁₀₀ × 6400

= ^{7 × 6400}/₁₀₀

= ⁴⁴⁸⁰⁰/₁₀₀ = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₈ years

∴ If the simple Interest is $2688, then the time = ¹/₄₄₈ × 2688 years

= ^{1 × 2688}/₄₄₈ years

= ²⁶⁸⁸/₄₄₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?

(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(6) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?

(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.