Number 76 A b and c please ebook Heinle Learning Ce D My Wil

ebook Heinle Learning Ce D My Wiley PLUS wil... P Pearson M Welcome Griffin D SO Go 162% double at the following annual inflation rates. (b) 6% (c) 8% (a) 3% (d) Check your answers using either the rule of 70 or the rule of 72, whichever applies. 76. Interest Allison Andrews invests $15,000 in an account pay- ing 7% per year compounded annually. (a) How many years are required for the compound amount to at least double? (Note that interest is only paid at the end of each year.) (b) In how many years will the amount at least triple? (c) Check your answer to part (a) using either the rule of 70 or the rule of 72, whichever applies. 77. Interest Andrea Davis plans to invest $600 into a money market account. Find the interest rate that is needed for the money to grow to $1240 in 14 years if the interest is com- pounded continuously. (Compare with Exercise 43 in the previous section.)

Solution

a) 15,000$ is invested at 7% compounded anually at the end of year;

Thus for it to double, let\'s consider the number of years = \'p\'
15,000 (1.07)^p= 15000*2
So (1.07)^p = 2 so eventually p = log 2 / log (1.07) = 0.6931/ 0.0676 = 10.2529
We\'ll round of 10.2529 to 11 years since the compounding is done only at te end of the year.
So, it takes 11 years for the sum to at least double

b) Similarly
15,000$ is invested at 7% compounded anually at the end of year;

Thus for it to triple, let\'s consider the number of years = \'q\'
15,000 (1.07)^q = 15000*3
So (1.07)^q = 3 so eventually q = log 3 / log (1.07) = 1.0986 / 0.0676 = 16.2514
We\'ll round of 16.2514 to 17 years since the compounding is done only at te end of the year.
So, it takes 17 years for the sum to at least double

c) For part \'a\' the rule of 72 applies since the annual rate of interest is between 4.9% and 11%
number of years to double = n = 72/r - This is rule of 72 (where \'r\' is the effective annual rate of interest)
In this case n = 72/7 = 10.1428 ~= 11 years
Hence our initial answer to part \'a\' of takign 11 years to at least double is correct