Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 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) = 10% per annum

Amount (A) = $11050

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 = $11050 – $6500 = $4550

Thus, Simple Interest = $4550

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 × 4550}/_{6500 × 10}

= ⁴⁵⁵⁰⁰⁰/₆₅₀₀₀

= 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) = 10% per annum

Simple Interest = $4550 (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 $6500

= ¹⁰/₁₀₀ × 6500

= ^{10 × 6500}/₁₀₀

= ⁶⁵⁰⁰⁰/₁₀₀ = 650

Thus, simple Interest for 1 year = $650

Now,

∵ If the simple Interest is $650, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₅₀ years

∴ If the simple Interest is $4550, then the time = ¹/₆₅₀ × 4550 years

= ^{1 × 4550}/₆₅₀ years

= ⁴⁵⁵⁰/₆₅₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(3) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?

(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(9) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(10) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.