Question

Keith received an excellent interest rate for his loan of $12,000. Calculate the nominal interest rate compounded semi-annually if the loan accumulated to $12,642.11 in 5 years and 6 months

Answer 1

$A=P(1+r/m)^{n}$

$m=2, n=2\times 5+1=11$

$12642.11=12000(1+r/m)^{11}$

$\frac{12642.11}{12000}= (1+r/2)^{11}$

$1.0535=(1+r/2)^{11}$

$1.0535^{\frac{1}{11}}=1+r/2$

$1.0047=1+r/2$

$0.0047=r/2$

$r=0.0094$