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 $10595 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6500

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

Amount (A) = $10595

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 = $10595 – $6500 = $4095

Thus, Simple Interest = $4095

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 × 4095}/_{6500 × 9}

= ⁴⁰⁹⁵⁰⁰/₅₈₅₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $4095 (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 $4095, then the time = ¹/₅₈₅ × 4095 years

= ^{1 × 4095}/₅₈₅ years

= ⁴⁰⁹⁵/₅₈₅ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(6) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?