Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $14000

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 = $14000 – $7000 = $7000

Thus, Simple Interest = $7000

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 × 7000}/_{7000 × 10}

= ⁷⁰⁰⁰⁰⁰/₇₀₀₀₀

= 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) = $7000

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

Simple Interest = $7000 (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 $7000

= ¹⁰/₁₀₀ × 7000

= ^{10 × 7000}/₁₀₀

= ⁷⁰⁰⁰⁰/₁₀₀ = 700

Thus, simple Interest for 1 year = $700

Now,

∵ If the simple Interest is $700, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₇₀₀ years

∴ If the simple Interest is $7000, then the time = ¹/₇₀₀ × 7000 years

= ^{1 × 7000}/₇₀₀ years

= ⁷⁰⁰⁰/₇₀₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.

(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(3) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(5) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.

(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(9) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.