Question

You are contemplating between four possible interest rate structures. The rates are as follows: annual effective rate of 12% annual nominal rate of 12% compounded monthly annual nominal rate of 8% compounded quarterly annual nominal rate of 10% compounded semiannually You wish to deposit $1,000 into a fund for 2 years. Calculate the difference between the largest and smallest possible accumulated values of your deposit at the end of 2 years.

Answer 1

Answer:

The difference between the largest and smallest possible accumulated values of the deposit at the end of 2 years is $98

Explanation:

Annual effective rate of 12%

FV = PV * (1+i)^n

FV = $1,000 * (1+0.12)^2

FV = $1,000 * 1.2544

FV = $1,254.

Annual nominal rate of 12% compounded monthly

FV = PV * (1+i)^nm

FV = $1,000 * (1+0.01)2^12

FV = $1,000 * (1+0.01)^24

FV = $1,000 * 1.2697

FV = $1,270

Annual nominal rate of 8% compounded quarterly

FV = PV * (1+i)^nm

FV = $1,000 * (1+0.02)2*4

FV = $1,000 * (1+0.02)^8

FV = $1,000 * 1.171659

FV = $1,172

Annual nominal rate of 10% compounded semiannually

FV = PV * (1+i)^n

FV = $1,000 * (1+0.05)^2*2

FV = $1,000 * (1+0.05)^4

FV = $1,000 * 1.215506

FV = $1,216

So, the difference between the largest and smallest possible accumulated values is $98 ($1,270 - $1,172)