An investment account was initiated with an investment of $1000. The fund had gr

Question

An investment account was initiated with an investment of $1000. The fund had grown to $1200 after one year, and an additional $1000 was invested. The fund balance at the end of two years was $2200.

(a) What annual effective interest rate was earned in the first year? What annual effective interest rate was earned in the second year?

(b) What was the equivalent time-weighted annual effective interest rate for the two years? (Answer: 9.54%)

(c) What equivalent annual effective interest rate was earned for the two years? (This is the dollar-weighted yield rate.) Calculate it exactly and also using the simple interest approximation. (Answer: 6.52%, 6.67%)

(d) Explain why the answer in (c) is smaller than the answer in (b)

Explanation / Answer

Answer (a) Annual effective interest rate in first year = (1200-1000)*100/1000 =20%

In second year, intial investment is 12000+ 1000 =2200, and at the end of 2nd year, amount is same 2200 hence its a 0% return in the second year

Answer (b) Euivalent time weighted annual effective interest rate for 2 years would be

= (1200/1000)*(2200/2200) = 1.2

Annual effective time weighted return per year = (1.2)^0.5 - 1 = 9.5445%

Answer (c) Annual effective interest rate for two years

1000= 200/(1+r) - 1000/(1+r) + 2200 (1+r)^2

Solving this r = 6.52%

Answer c is lower than answer b because answer b is based on time weights wherein duration of investment is an important factor.

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