Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $12400

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 = $12400 – $6200 = $6200

Thus, Simple Interest = $6200

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 × 6200}/_{6200 × 10}

= ⁶²⁰⁰⁰⁰/₆₂₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6200

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

Simple Interest = $6200 (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 $6200

= ¹⁰/₁₀₀ × 6200

= ^{10 × 6200}/₁₀₀

= ⁶²⁰⁰⁰/₁₀₀ = 620

Thus, simple Interest for 1 year = $620

Now,

∵ If the simple Interest is $620, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₀ years

∴ If the simple Interest is $6200, then the time = ¹/₆₂₀ × 6200 years

= ^{1 × 6200}/₆₂₀ years

= ⁶²⁰⁰/₆₂₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(2) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(9) 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.

(10) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?