Question

Problem541

a.FindtheFVof$1,500investedtoearn15%after5years.

c.FindthePVof$1,500duein5yearsifthediscountrateis5%.

d.Asecurityhasacostof$1,500andwillreturn$2,000after10years.Whatrateofreturndoesthesecurityprovide?

e.SupposeCalifornia’spopulationis38.5millionpeople,anditspopulationisexpectedtogrowby2%annually.Howlongwillittakeforthepopulationtodouble?

f.FindthePVofanordinaryannuitythatpays$2,000eachofthenext10yearsiftheinterestrateis10%.ThenfindtheFVofthatsameannuity.

g.HowwillthePVandFVoftheannuitychangeifitisanannuitydueratherthananordinaryannuity?

i.Findtheannualpaymentsforanordinaryannuityandanannuityduefor10yearswithaPVof$1,500andaninterestrateof10%

Answer 1

Answer : (a.) Calculation of Future Value

Future Value = Present Value * (1 + rate)^number of years

= 1500 * (1 + 0.15)^5

= 1500 * 2.011357

= 3017.04

(b.) Calculation of Present Value

Present Value = Future Value * (1 + rate)^number of years

= 1500 / (1 + 0.05)^5

= 1500 / 1.276282

= 1175.29

(c.) To calculate Rate of return we will equate 1500 to 2000 after 10 years and find rate value

Let r be the rate of return on investment

1500 = 2000 / (1 + r)^10

On solving r is 2.92%

(d.) Calculation of time in which Calciformia Population will double

(38.5 * 2) = 38.5 * (1 + 0.02)^n

77 = 38.5 * (1 + 0.02)^n

Solving for n

n = 35 years