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*1.05^{n}

=> 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*1.09^{n}

=> 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*1.20^{n}

=> 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*1.02^{n}

=> n = ln(78.76/53) / ln(1.02) = 20 years

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