Question

TIME FOR A LUMP SUM TO DOUBLE How long will it take $700 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.

5%.

year(s)

13%.

year(s)

17%.

year(s)

100%.

year(s)

Answer 1

(a) Interest Rate = 5 %

Let time required be T1

Initial Investment = $ 700

Final Value = $ 1400

700 x (1.05)^(T1) = 1400

(1.05)^(T1) = 1400 / 700

T1 = $\log_{1.05}2$ = 14.21 years

(b)

Interest Rate = 13 %

Let time required be T2

Initial Investment = $ 700

Final Value = $ 1400

700 x (1.13)^(T1) = 1400

(1.13)^(T2) = 1400 / 700

T2 = $\log_{1.13}2$ = 5.67 years

(c)

Interest Rate = 17 %

Let time required be T3

Initial Investment = $ 700

Final Value = $ 1400

700 x (1.05)^(T2) = 1400

(1.17)^(T2) = 1400 / 700

T2 = $\log_{1.17}2$ = 4.42 years

(d)

Interest Rate = 100 %

Let time required be T4

Initial Investment = $ 700

Final Value = $ 1400

700 x (1+1)^(T1) = 1400

(2)^(T1) = 1400 / 700

T1 = $\log_{2}2$ = 1 year