Question

(Compound

value solving for

n​)

How many years will the following​ take?a.

​$500

to grow to

​$1,039.50

if invested at

5

percent compounded annuallyb.

​$35

to grow to

​$53.87

if invested at

9

percent compounded annuallyc.

​$100

to grow to

​$298.60

if invested at

20

percent compounded annuallyd.

​$53

to grow to

​$78.76

if invested at

2

percent compounded annuallya. How many years will it take for

​$500

to grow to

​$1,039.50

if invested at

5

percent compounded​ annually?

nothing

years ​ (Round to the nearest whole​ number.)b. How many years will it take for

​$35

to grow to

​$53.87

if invested at

9

percent compounded​ annually?

nothing

years  ​(Round to the nearest whole​ number.)c. How many years will it take for

​$100

to grow to

​$298.60

if invested at

20

percent compounded​ annually?

nothing

years ​ (Round to the nearest whole​ number.)d. How many years will it take for

​$53

to grow to

​$78.76

if invested at

2

percent compounded​ annually?

nothing

years ​ (Round to the nearest whole​ number.)

Answer 1

(a) Let number of years be n
Present Value = PV = 500
Future Value = FV = 1,039.50
Interest rate = r = 5% or 0.05
FV = PV(1+r)ⁿ
=> 1,039.50 = 500*1.05ⁿ
=> n = ln(1,039.50/500) / ln(1.05) = 15 years

(b) Let number of years be n
Present Value = PV = 35
Future Value = FV = 53.87
Interest rate = r = 9% or 0.09
FV = PV(1+r)ⁿ
=> 53.87 = 35*1.09ⁿ
=> n = ln(53.87/35) / ln(1.09) = 5 years

(c) Let number of years be n
Present Value = PV = 100
Future Value = FV = 298.60
Interest rate = r = 20% or 0.20
FV = PV(1+r)ⁿ
=> 298.60 = 100*1.20ⁿ
=> n = ln(298.60/100) / ln(1.20) = 6 years

(d) Let number of years be n
Present Value = PV = 53
Future Value = FV = 78.76
Interest rate = r = 2% or 0.02
FV = PV(1+r)ⁿ
=> 78.76 = 53*1.02ⁿ
=> n = ln(78.76/53) / ln(1.02) = 20 years