Answer:
Step-by-step explanation:
PV = $2500
r = 6%
Compounded semi annually for ten years => number of periods: 10*2 = 20
a. the balance of account at end of peroid (FV)
FV = PV [tex](1+r)^{n}[/tex] = 2500[tex](1+0.06)^{20}[/tex] = 8017.8386
b. How much interest is earned; FV - PV = 8017.8386 - 2500 = 5517.8686
c. what is effective rate of interest :
Answer:
The answers to the question are
a) The balance of account at end of period $4515.278
b) The interest earned $2515.278
c) The effective rate of interest is 0.0609 or 6.09 %
Step-by-step explanation:
To solve the question
a) Here we have the compound interest formula given by
[tex]A = P(1+\frac{r}{n})^{nt}[/tex] Where,
P = Initial investment = $2500
r = Annual interest rate = 6% =0.06
n = Number of compounding periods per year = 2
t = Number of years 10
From which we have
[tex]A = 2500*(1+\frac{0.06}{2})^{2*10}= 2500(1.03)^{20}[/tex] = $4515.278
The balance of account at end of period $4515.278
b) Interest earned = Balance - initial investment = $4515.278 - $2500 = $2515.278
c)
The effective interest rate is the interest rate that accrues to an investment or loan as a result of the compounding the interest for a given time period of time. It is also known as the effective annual interest rate
The effective rate of interest is given by
Effective rate = [tex](1+\frac{r}{n} )^n -1[/tex]Where
r = Annual interest rate
n = Number of annual compounding periods
this gives [tex](1+\frac{0.06}{2} )^{2} -1[/tex] = 0.0609 = 6.09 %
