Question

Suppose you had £10,000 to invest for five years. You are deciding between a savings account at Fidelity that will pay a 7% annual interest rate compounded daily (Fidelity) and one at Raymond James that will also pay 7% but compounded monthly (Raymond James). You are about to invest with Fidelity but then you realize there are some fees attached to this product. Raymond James has no fees. What is your point of indifference? In other words, how much could Fidelity charge before its advantage in compounding is exactly balanced by its fee? Show and explain all supporting calculations.   

Answer 1

Solution

Future value=Initail investment*(1+r)^n

where

r-intrest rate per period

n-number of periods

For Fidelity

Using 365 days a year

r-7/365=0.019178% per days

n-365*5=1825

Putting values

Future value(Fidelity)=10000*(1+.00019178)^1825=14190.18

Now for Raymond

r-7/12=0.583333% per month

Number of periods=12*5=60

Putting values

Future value(Raymond)=10000*(1+.00583333)^60=14176.25

Therefore the amount Fidelity charge before its advantage in compounding is exactly balanced by its fee=14190.18-14176.25=$13.93

If you are satisfied with the answer,please give a thumbs up