[Financial Mathematics;Theory of Interest and Life Contingencies] A trust compan

Question

[Financial Mathematics;Theory of Interest and Life Contingencies] A trust company pays 7% efective on deposits at the end of each year. At the end of every four years, a 5% bonus is paid on the balance at that time. Find the efective rate of interest earned by an investor if he leaves his money on deposit for (a) 3 years; (b) 4 years; (c) 5 years [Financial Mathematics;Theory of Interest and Life Contingencies] A trust company pays 7% efective on deposits at the end of each year. At the end of every four years, a 5% bonus is paid on the balance at that time. Find the efective rate of interest earned by an investor if he leaves his money on deposit for (a) 3 years; (b) 4 years; (c) 5 years [Financial Mathematics;Theory of Interest and Life Contingencies] A trust company pays 7% efective on deposits at the end of each year. At the end of every four years, a 5% bonus is paid on the balance at that time. Find the efective rate of interest earned by an investor if he leaves his money on deposit for (a) 3 years; (b) 4 years; (c) 5 years

Explanation / Answer

(1) Effective rate of interest on 3 years deposit:

     r = (1+i)n - 1, where r = effective rate of interest; i = nominal rate of interest i.e 7%; n= no. of periods ie.3.

       = (1+07)3 - 1 = 1.23 -1 = 0.23 for 3years or 0.0767 or 7.67% for 1 year

Hence, effective rate of interest is 7.67%

(2) Effective rate of interest on 4 yenar deposit:

      r = (1+i)n - 1 = (1+0.07)4 - 1 = 1.31 -1 = 0.31

      Bonus = 1.31 x 5% = 0.07

      Total return in 4 years = 0.31 + 0.07 = 0.38 in 4 years, annual return is 0.38/4 = 0.095 or 9.5%

       Hence, effeective rate of interest = 9.5%

(3) Effective rate of interest on 5 years deposit:

      r = (1+i)n - 1

      r = (1+0.07)4- 1 = 1.31 - 1 = 0.31 interest

      Bonus = 1.31 x 0.05 = 0.07

      Total benefit at the end of 4th year = 0.31 + 0.07 = 0.38

      interest for 5th year = (1.31+0.07) (1+0.07)1 - (1.31+0.07) = 0.10

      Total benefit for 5 years = Interest for first 4 years + Bonus at the end of 4 years + 5th year interest

                                             = 0.31 + 0.07 + 0.10 = 0.48

      Hence, effective interest per annum = 0.48/5 = 0.096 = 9.6%

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