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 $10010 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10010

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 = $10010 – $6500 = $3510

Thus, Simple Interest = $3510

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 × 3510}/_{6500 × 9}

= ³⁵¹⁰⁰⁰/₅₈₅₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $3510 (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 $3510, then the time = ¹/₅₈₅ × 3510 years

= ^{1 × 3510}/₅₈₅ years

= ³⁵¹⁰/₅₈₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(8) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.