Question

3a. An insurance company is offering quarterly payments of $580 for the next 20 years in exchange for a one-time payment of $16,000 today. What is the per annum rate of return on this offer? (Round to nearest 100th of a percent and enter your answer as a percentage, for example, as 12.34)

Answer:

3b. What is the future value (at the end of 10 years) of an annuity that pays $3200 a quarter over 10 years with the payments invested at 8.3% per annum (assume compounding matches payment periods, common assumption for such problems)? (enter your answer in the following format 123456.78)

Answer:

3c. Jack and Jill need to save $6100 toward a new car. How long will it take them if they save $200 a month earning interest at 4.7% per year? (Treat as an ordinary annuity.) (State your answer in years rounded to the second decimal place, e.g., 12.34)

Answer:

Answer 1

3a)
Nper = 20 * 4 = 80
PMT = 580
PV = 16000
FV = 0

Rate of return can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(80,580,-16000,0)*4
= 13.48%

Rate of return = 13.48%

3b)
Nper = 10 * 4 = 40
Rate = 8.3% / 4 = 2.075%
PMT = 3200
PV = 0

Future value can be calculated by using the following excel formula:
=FV(rate,nper,pmt,pv)
=FV(2.075%,40,-3200,0)
= $196,460.24

Future value = $196,460.24

3c)
FV = 6100
PMT = 200
Rate = 4.7% / 12
PV = 0

Number of years can be calculated by using the following excel formula:
=NPER(rate,pmt,pv,fv)
=NPER(4.7%/12,200,0,-6100)/12
= 2.41 years

Number of years = 2.41 years