Answer:
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[tex](1+\frac{r}{n} )^{nt}[/tex]
Substituting the known values , we get
A = 1000 x [tex](1 + \frac{0.0675}{2} )^{2 * 15}[/tex]
= $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 [tex](1 + 0.0675)^{15}[/tex]
= 2663.90
Hence interest earned = $2663.90 - $ 1000
= 1663.90
