Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6500

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12350

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 = $12350 – $6500 = $5850

Thus, Simple Interest = $5850

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 × 5850}/_{6500 × 9}

= ⁵⁸⁵⁰⁰⁰/₅₈₅₀₀

= 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) = $6500

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $5850 (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 = 9% of Principal

= 9% of $6500

= ⁹/₁₀₀ × 6500

= ^{9 × 6500}/₁₀₀

= ⁵⁸⁵⁰⁰/₁₀₀ = 585

Thus, simple Interest for 1 year = $585

Now,

∵ If the simple Interest is $585, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₈₅ years

∴ If the simple Interest is $5850, then the time = ¹/₅₈₅ × 5850 years

= ^{1 × 5850}/₅₈₅ years

= ⁵⁸⁵⁰/₅₈₅ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.

(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?

(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(10) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.