Question

For 50,000, Kelly purchases an annuity-immediate that pays 400 monthly for the next 20 years. Calculate the annual nominal interest rate convertible monthly earned by Kelly's investment.

(Don't use Excel)

Answer 1

Amount of Equal payment annuity=	400
Amount paid for annuity (P)=	50000
Total months in 20 years (n)=20*12=	240
Annuity or Equal payments formula = P* i *((1+i)^n)/(((1+i)^n)-1)
400 = 50000*i*((1+i)^240)/(((1+i)^240)-1)
We will Assume ínterest rate per month is 0.6% or	0.006
50000*0.006*((1+0.006)^240)/(((1+0.006)^240)-1)
393.6746495
We will Assume ínterest rate per month is 0.7% or	0.007
50000*0.007*((1+0.007)^240)/(((1+0.007)^240)-1)
430.7522477
Actual Payment is in between two payments calculated by i. so We will calculate (i) by interpolation formula
interpolation formula = uper rate - (uper rate - lower rate)*(Uper value - actual value)/(uper value - lower value)
0.007 - ((0.007-0.006)*(430.7522477-400)/(430.752247-393.6746495)
0.007-	0.00082940
0.00617060
Per month rate is 0.00617060
So annual Rate is 0.00617060*12=	0.07405

So nominal annual rate is 7.405 or 7.41% convertible semiannually