Simple Interest
Math MCQs

Question :    Betty took a loan of $6500 at the rate of 7% 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  10

Solution & Explanation

Solution

Given,

Principal (P) = $6500

Rate of Simple Interest (R) = 7% 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 × 7}

= ⁴⁵⁵⁰⁰⁰/₄₅₅₀₀

= 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) = 7% 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 = 7% of Principal

= 7% of $6500

= ⁷/₁₀₀ × 6500

= ^{7 × 6500}/₁₀₀

= ⁴⁵⁵⁰⁰/₁₀₀ = 455

Thus, simple Interest for 1 year = $455

Now,

∵ If the simple Interest is $455, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₅ years

∴ If the simple Interest is $4550, then the time = ¹/₄₅₅ × 4550 years

= ^{1 × 4550}/₄₅₅ years

= ⁴⁵⁵⁰/₄₅₅ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(3) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?

(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(7) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(10) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?