K7000 is paid at the end of each quarter into an account which bearing interest compounded quarterly. If he annuity accrues to K10000 over five years, deermine the nominal interest rate
To determine the nominal interest rate, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n),
where:
- FV is the future value of the annuity (K10000),
- P is the regular payment at the end of each quarter (K7000),
- r is the nominal interest rate to be found,
- n is the number of compounding periods per year (4 for quarterly compounding), and
- t is the number of years the annuity is held (5 years).
Plugging in the given values and solving for r, we get:
K10000 = K7000 * ((1 + r/4)^(4*5) - 1) / (r/4).
Solving for r, we find the nominal interest rate:
10000 = 7000 * ((1 + r/4)^20 - 1) / (r/4)
1.42857143 = (1 + r/4)^20 - 1
(1 + r/4)^20 = 2.42857143
1 + r/4 = (2.42857143)^(1/20)
1 + r/4 = 1.05107008
r/4 = 0.05107008
r = 0.20428032
Therefore, the nominal interest rate is approximately 20.43% per year.