Question

Suppose that you invest $100 in an account for 20 years. This account will credit you 5% annual effective rate of interest for the first 5 years, 5% annual effective rate of discount for the second 5 years, 5% simple rate of interest for the third 5 years and 5% simple rate of discount for the last 5 years. How much money will you have at the end of 20 years?

Answer 1

Invested $100 for 20 years.

Amount at the end of first 5 years if we add 5% annual rate of interest every year :

1st year - 100+5% = 105

2nd year - 105+5% = 110.25

3rd year - 110.25+5% = 115.76

4th year - 115.76+5% = 121.55

5th year - 121.55+5% = 127.63

Amount at the end of second 5 years if we discount 5% annual rate every year :

6th year - 127.63-5% = 121.25

7th year - 121.25-5% = 115.19

8th year - 115.19-5% = 109.43

9th year - 109.43-5% = 103.96

10th year - 103.96-5% = 98.76

Amount at the end of third 5 years if we add 5% annual rate of interest every year :

11th year - 98.76+5% = 103.70

12th year - 103.70+5% = 108.88

13th year - 108.88+5% = 114.33

14th year - 114.33+5% = 120

15th year - 120+5% = 126

Amount at the end of last 5 years if we discount 5% annual rate every year :

16th year - 126-5% = 119.7

17th year - 119.7-5% = 113.72

18th year - 113.72-5% = 108.03

19th year - 108.03-5% = 102.63

20th year - 102.63-5% = 97.50

so at the end of 20 years, we will get $97.5