7. Riley invested $1,000 in savings
bonds. If the bonds earn 6.75% interes
compounded semi-annually, how
much interest will Riley earn in 15
years?
A $1567.32
B $163.90
C $1663.90
D $1632.22

Riley will earn interest of $1706.86 in 15 years. But when the same problem solved for interest compounded annually we get,

c)1663.90

The options does not match with answer

Step-by-step explanation:

Given

principal amount P = $ 1000

rate of interest r = 6.75 % = 6.75/100 =0.0675

time t = 15

compounded semi annually, hence

no. of times interest is compounded, n = 2

We know that the formula for deriving final amount (A) is

A = P

Substituting the known values , we get

A = 1000 x

   = $2706.86

Hence the interest earned = A - P

                                             = $2706.86 -  $ 1000

                                             = $1706.86

The answer is  $1706.86

But when the same problem solved for interest compounded annually we get, n=1 and so

A = 1000 x  

   = 2663.90

Hence interest earned = $2663.90 -  $ 1000

                                       = 1663.90

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