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ECON1003 S1 2023

PROBLEM SET 6

1.         Find the value of the 50th term of the series:  50 + 56 + 62 + 68 +.......

2.         Find the sum of the first seven terms of the series:  2 + 4 + 8 + 16 +.......

3.         5 + x + 80 are three successive terms of a GP.  Find x.

4. Two rival small firms, ExcelPC and PCword, service computers. In 1996, ExcelPC has a monthly turnover of 1200 computers, while PCword services 800 computers monthly.  Use series to determine the month in which ExcelPC’s turnover first exceeds that of PCword if

the monthly turnover is projected according to the following plans:

Plan 1:  ExcelPC reduces its output by 60 each month while PCword increases output by 100 each month.

Plan 2:  ExcelPC reduces output by 5% each month while PCword increases output by 2% each month.

Assume the changes are first implemented in month 2.

5.

a. A sum of £5000 is borrowed for two years at 8% compound interest per year. Calculate the total amount owed after two years.

b. Calculate the number of years that it takes £5000 to grow to £12000 at an interest rate of 8% compounded annually

6. If £950 is invested at 7.5%

i. simple interest   ii. compounded 4 times a year   iii. compounded continuously calculate (a)       the value of the investment at the end 5 years

(b)       the number of years that the investment should be left on deposit if it is to

double in value

7. If an investment of £500 grows to £750 when invested at an annual rate of interest of i% (continuous compounding) for 8 years, calculate i.