Question

Compound

value solving for

n​)

How many years will the following​ take?a.

​$510

to grow to

​$1,093.23

if invested at

10

percent compounded annuallyb.

​$38

to grow to

​$60.30

if invested at

8

percent compounded annuallyc.

​$110

to grow to

​$421.94

if invested at

13

percent compounded annuallyd.

​$51

to grow to

​$64.39

if invested at

6

percent compounded annually

a. How many years will it take for

​$510

to grow to

​$1,093.23

if invested at

10

percent compounded​ annually?

nothing

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

​$38

to grow to

​$60.30

if invested at

8

percent compounded​ annually?

nothing

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

​$110

to grow to

​$421.94

if invested at

13

percent compounded​ annually?

nothing

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

​$51

to grow to

​$64.39

if invested at

6

percent compounded​ annually?

nothing

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

Answer 1

(a) Let number of years be n
Present Value = PV = 510
Future Value = FV = 1093.23
Interest rate = r = 10% or 0.10
FV = PV(1+r)ⁿ
=> 1093.23 = 510*1.1ⁿ
=> n = ln(1093.23/510) / ln(1.1) = 8 years

(b) Let number of years be n
Present Value = PV = 38
Future Value = FV = 60.30
Interest rate = r = 8% or 0.08
FV = PV(1+r)ⁿ
=> 60.30 = 38*1.08ⁿ
=> n = ln(60.30/38) / ln(1.08) = 6 years

(c) Let number of years be n
Present Value = PV = 110
Future Value = FV = 421.94
Interest rate = r = 13% or 0.13
FV = PV(1+r)ⁿ
=> 421.94 = 110*1.13ⁿ
=> n = ln(421.94/110) / ln(1.13) = 11 years

(d) Let number of years be n
Present Value = PV = 51
Future Value = FV = 64.39
Interest rate = r = 6% or 0.06
FV = PV(1+r)ⁿ
=> 64.39 = 51*1.06ⁿ
=> n = ln(64.39/51) / ln(1.06) = 4 years