A friend has $900 that he has saved from his part-time job. He will need his money, plus any interest earned on it, in six months and has asked for your help in deciding whether to put the money in a bank savings account at 4.80% interest or to lend it to Victor. Victor has promised to repay $936 after six months. Required: Calculate the interest earned on the savings account for six months. (Round your answer to 2 decimal places.) Calculate the annual rate of return if the money is lent to Victor. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Which alternative would you recommend?

a) Hi, first let´s find the future value if the money is left in a savings account at 4.8% annual, for 6 months. Since the interest rate is annual, we have to convert the semesters into years, that is 1/2= 0.5 years.

Now, we have to use the following formula in order to find the future value o leaving the money into a savings account.

[tex]FutureValue=PresentValue*(1+r)^{n}[/tex]

Everything should look like this}

[tex]FutureValue=900*(1+0.048)^{0.5}=921.35[/tex]

As you can see, if you choose to leave your money in the bank, you will get $21.35 in interest ($921.35 - $900 = $21.35), so it is better to lend this money to Victor ($936 - $900 = $36 in interest)

b) In order to find the rate of return that Victor is paying, we need to do the following.

[tex]r=\frac{FutureValue}{PresentValue} -1=\frac{936}{900} -1=0.04[/tex]

Therefore Victor is paying 4%, but 4% effective semi-annually, and we need this rate to be annual, so we use the following formula.

[tex]r(annual)=(1+r(semi-annual))^{2} -1=(1+0.04)^{2} -1=0.0816[/tex]

So the effective annual rate that Victor is paying you is 8.16%

Best of luck.