Question

For a 10 year deposit, what interest rate payable annually is equivalent to 5% interest payable quarterly ​

Answer 1

Given :  a 10 year deposit   5% interest payable quarterly ​

To find :  equivalent  interest rate payable annually

Solution:

Let say amount = P

Rate of interest = R

Time  n = 10 Years

A =  P(1 + R/100)ⁿ

=> A = P(1 + R/100)¹⁰

R = 5%

payable quarterly ​

=> Quarterly interest rate = 5/4 = 1.25 %

Time = n = 10 * 4 = 40 Quarters

A = P(1 + 1..25/100)⁴⁰

=> A = P( 1.0125)⁴⁰

P(1 + R/100)¹⁰ = P( 1.0125)⁴⁰

=> (1 + R/100)¹⁰ = ( 1.0125)⁴⁰

=>  (1 + R/100)¹⁰  = ((1.0125)⁴)¹⁰

=> 1 + R/100 = 1..050945

=> R/100 = 0.050945

=> R = 5.0945

5.0945 % interest rate payable annually is equivalent to 5% interest payable quarterly ​ for a 10 year deposit

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