Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10880

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 = $10880 – $6400 = $4480

Thus, Simple Interest = $4480

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 × 4480}/_{6400 × 10}

= ⁴⁴⁸⁰⁰⁰/₆₄₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 10% per annum

Simple Interest = $4480 (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 = 10% of Principal

= 10% of $6400

= ¹⁰/₁₀₀ × 6400

= ^{10 × 6400}/₁₀₀

= ⁶⁴⁰⁰⁰/₁₀₀ = 640

Thus, simple Interest for 1 year = $640

Now,

∵ If the simple Interest is $640, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₄₀ years

∴ If the simple Interest is $4480, then the time = ¹/₆₄₀ × 4480 years

= ^{1 × 4480}/₆₄₀ years

= ⁴⁴⁸⁰/₆₄₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?

(3) 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.

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?