You want to invest your savings of $30,000 in government securities for the next

Question

You want to invest your savings of $30,000 in government securities for the next 2 years. Currently, you can invest either in a security that pays interest of 8.4 percent per year for the next 2 years or in a security that matures in 1 year but pays only 5.8 percent interest. If you make the latter choice, you would then reinvest your savings at the end of the first year for another year.

If you choose the 2-year security, the value of your savings after the second year will be? Answer: $35, 252.00

If you choose to invest in the 1-year security, the value of your savings after the first year will be? Answer: $31,740.00

To do as well as you would with the first choice, during the second year the 1-year security would have to earn??????

Explanation / Answer

Option 1: 8.4 percent per year for the next 2 years

So Under this option basically your $30,000 will grow at 8.4% p.a.

So after one year the amount would be 30,000+8.4%=32520(30000+2520)

and assuming that the whole investment including Interest of Year 1 is eligible for reinvestment then we have the following investment eligible for interest

32520+8.4%=35251.68(32520+2731.68)

Can be rounded upto $35,252

Option 2: security that matures in 1 year but pays only 5.8 percent interest

Investment=30,000

so we are investing for 1 year at 5.8%

so we get, 30,000+5.8%=$31,740 (30000+1740)

Now as per your question, the rate required for Option 2 to earn at the end of second year will be the difference between final answer of option 1 and 2 so it will be as follow:

Difference =$3,512 (35252-31740)

now let us calculate the rate of interest required for Option 2 to earn in second year

=3512/31740*100

=11.06490233144297

rounded off to 11.06%

Hence the rate of interest required for the option 2 to earn in second year is =11.06%

Plz Rate

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