Question

What is the annual percentage yield(APY) for money invested at an annual rate of
A.) 5.15% compounded continuously?
B.) 5.20% compounded semiannually?

Answer 1

A.) 5.15% compounded continuously?

Answer 2

Annual percentage yield(APY) for money invested at an annual rate of

A.  5.15% compounded continuously is equals to 5.3%

B. 5.20% compounded semiannually is equals to 5.23%

What is Annual percentage yield(APY) ?

" Annual percentage yield(APY) is defined as percentage which reflects the interest amount invested in the bank for a period of one year."

Formula used

$A = Pe^{rt}$

A = Final amount

P = Initial Principal

r = rate of interest

t= time

According to the question,

Given,

A. Rate of interest 'r' compounded continuously= 5.15%

                                                                             = 0.0515

Here take Principal 'P'=1

                 time 't' =1 year

Substitute the value in the formula of Annual percentage yield(APY) we get,

$A = (1) e^{0.0515}$

   $= 1.05284$

   ≈ 1.053

Annual rate of return = (A - P) 100

                                    = (1.053 - 1)100

                                   = 0.053 × 100

                                   = 5.3%

B. Rate of interest 'r' compounded semiannually = 5.20%

                                                                                   = 0.052

$A = P( 1+ \frac{r}{n} )^{nt}$

P = 1

t = 1

n = 2

Substitute the value in the formula Annual percentage yield(APY) we get,

$A = 1( 1+ \frac{0.052}{2} )^{2}$

  $= (1 + 0.026)^{2} \\= 1.05226$

Annual rate of return = (A - P) 100

                                  = (1.05226 -1)100

                                  = (0.05226)100

                                  = 5.23%

Hence, annual percentage yield(APY) for money invested at an annual rate of

A.  5.15% compounded continuously is equals to 5.3%

B. 5.20% compounded semiannually is equals to 5.23%

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