Question

You have $5,000 to invest. You have two choices of how to invest. Choice “A” would have you invest at 5% per year for two years. Choice “B” would have you invest at 4.75% for the first year and then re-invest the proceeds for another year. What rate of return would you need to earn on the second year of Choice “B” to make you expect to earn the same return as for Choice “A”?

Answer 1

Option A:

Principal = $ 5,000

Interest Rate = 5%

Time = 2 years

  

= $ 500

Amount after two years = Prinicpal + Interest = $ 5,000 + $ 500 = $ 5,500

Option B:

Principal = $ 5,000

Interest rate for 1 year = 4.75 %

Time = 1 year

  

= 237.5

Proceeds = Principal + Interest after 1 year

= $ 5,000 + $ 237.5

= $ 5237.5

As per question, the amount after two years should be same.

Hence, interest required in second year for Option B = $ 5,500 - $ 5,237.5

= $ 262.5

In order to get interest = $ 262.5 , we need to find the interest rate

By rearranging the aboe formula, we get

   // Principal will be $ 5237.5 as proceeds are re-invested for 1 year

= 0.050119 * 100

= 5.01 %