Question

# (Compound value solving for n​) How many years will the following​ take?a. ​\$500 to grow to...

(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.)

(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

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