$50,000 invested at an interest rate of 6 percent compounded monthly can be represented by the function . Use this equation to answer Parts A and B. Part A What will be the value of A(t) after 4 years? Part B How long will it take for the initial amount to increase by $20,000?

Part A

$63,524

Part B

67.5 months or 5 years 7 months

Explanation:

Future value is the sum of value of principal invested and compounded return received over the investment period.

Using following formula of future value to calculate the required interest rate.

FV  = PV x ( 1 + r )^n

Part A

PV  = Present value = $50,000

n = number of years = 4 years

r = Interest rate = 6%

FV = Future value = ?

FV = 50,000 x ( 1 + 0.06/12 )^4*12

FV = $63,524

Part B

PV  = Present value = $50,000

r = Interest rate = 6%

FV = Future value = 50,000+20,000 = $70,000

n = number of years = ?

$70,000 = 50,000 x ( 1 + 0.06/12 )^n

$70,000 / 50,000 = 1.005^n

1.4 = 1.005 n

log 1.4 = n log 1.005

n = log 1.4 / log 1.005

n = 67.5 months

n = 5 years 7 months

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