Compound interest with non-annual periods) You just received a bonus of $2,000.

Question

Compound interest with non-annual periods) You just received a bonus of $2,000.

a.Calculate the future value of $2,000, given that it will be held in the bank for 6 years and earn an annual interest rate of 4 percent.

b.Recalculate part (a) using a compounding period that is (1) semiannual and (2) bimonthly.

c.Recalculate parts (a) and (b) using an annual interest rate of 8 percent.

d.Recalculate part (a) using a time horizon of 12 years at an annual interest rate of 4 percent.

e.What conclusions can you draw when you compare the answers in parts (c) and (d) with the answers in parts (a) and (b)?

a.What is the future value of $2,000 in a bank account for 6 years at an annual interest rate of 4 percent?

$ (Round to the nearest cent.)

Explanation / Answer

a. Calculate the future value of $2,000, given that it will be held in the bank for 6 years and earn an annual interest rate of 4 percent. Sol a : Bonus $2,000 Principle amount $2,000 Interest Rate 4% Time 6 Formula: FV = PV(1+r)^t 2000*(1+0.04)^6 = $2,531 b. Recalculate part (a) using a compounding period that is (1) semiannual and (2) bimonthly. Solb: Semiannual FV = PV(1+r/m)^t*m 2000*(1+(0.04/2))^(6*2) = $2,536 bimonthly FV = PV(1+r/m)^t*m 2000*(1+(0.04/6))^(6*6) = $2,540 c. Recalculate parts (a) and (b) using an annual interest rate of 8 percent. Solc Principle amount $2,000 Interest Rate 8% Time 6 Annually FV = PV(1+r)^t 2000*(1+0.08)^6 = $3,174 Semiannual FV = PV(1+r/m)^t*m 2000*(1+(0.08/2))^(6*2) = $3,202 bimonthly FV = PV(1+r/m)^t*m 2000*(1+(0.08/6))^(6*6) = $3,222 d. Recalculate part (a) using a time horizon of 12 years at an annual interest rate of 4 percent. Sold Principle amount $2,000 Interest Rate 4% Time 12 FV = PV(1+r)^t 2000*(1+0.04)^12 = $3,202 e. What conclusions can you draw when you compare the answers in parts (c) and (d) with the answers in parts (a) and (b) Sol e. The conclusions clearly states that with rise in interest rates along with the time to maturity, the future value of the underlying assets also increases. here, bimonthly >semiannual>annual

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