Question

19. Bo has $200 and is considering two different investment opportunities for his money. The first option is a savings account that will yield $264.50 after 2 years of compound annual interest. The second option is a short-term bond that will yield $234 after only 1 year. If the annual inflation rate is 3%, which of these two options has a higher real interest rate? a. Option 1 b. Option 2 c. They are equal and negative d. They are equal and positive

Can you please explain to me how you arrive at the answer of B? I'm confused.

Answer 1

option 1

If the money is kept in savings account

Total amount = 264.5

Nominal interest rate = r

Principal = 200 = P

Number of years = n = 2

Compound interest = 264.5-200 = 64.5$

CI = P (1+r)ⁿ​​​​​-P

64.5 = 200(1+r)²-200

(264.5/200)= (1+r)²

(1+r) = (1.3225)^1/2

(1+r) = 1.15

r = 0.15

r = 15%

Nominal interest rate = 15%

Real interest rate = Nominal interest rate - inflation rate

Real interest rate = 15-3 = 12%

Option 2

Bond maturity value =234$

Bond value = $200

Nominal interest rate = r

N = number of years = 1

Bond maturity value = Bond value (1+r)ⁿ

234=200(1+r)

1+r = 1.17

r = 0.17

r = 17%

Nominal interest rate = 17%

Real interest rate = Nominal interest rate-- inflation rate

Real interest rate = 17-3 = 14%

So in option 2 the real interest is higher which means the rate of return is higher.