Compound Interest. Suppose $5000 is invested in a start-up enterprise estimated

Question

Compound Interest. Suppose $5000 is invested in a start-up enterprise estimated return at an annual rate of 6%. How much will the investment be worth after 5 years if the interest is compounded quarterly? What is the Annual Percentage Yield in case a? How much will the investment be worth after 5 years if the interest is compounded continuously? What is the Annual Percentage Yield in case c? How long will it take for the investment to double if the interest is compounded continuously? a. b. c. d. e.

Explanation / Answer

As per FV formula,

FV = PV x (1+r/n)^nt

a) Here FV =?, PV $5000, r = 6%, n = 4, t = 5

FV = 5000 x (1+6%/4)^4*5

FV = 5000 x 1.34686

FV = $6,734.30

b) APY = (1+r/n)^n-1

APY = (1+6%/4)^4-1

APY = 6.14%

For compounded continuously,

FV = PV x e^rt

c) FV = 5000 x e^(.06*5)

FV = 5000 x 1.34986

Fv = $6,749.30

d) APY , 6749.30 =5000x (1+APY)^5

1.34986 = (1+APY)^5

1.06183 = 1+APY

APY = 6.18%

e) Using the same formula FV = PV x e^rt

10000 = 5000 x e ^.06t

e^.06t = 2

taking log both side

.06t = 0.3010/0.4342

T = 11.55 yrs

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