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 $13300 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $13300

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 = $13300 – $7000 = $6300

Thus, Simple Interest = $6300

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 × 6300}/_{7000 × 10}

= ⁶³⁰⁰⁰⁰/₇₀₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $6300 (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 $6300, then the time = ¹/₇₀₀ × 6300 years

= ^{1 × 6300}/₇₀₀ years

= ⁶³⁰⁰/₇₀₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?

(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?