Question

Calculate the number of years for an unvestment if $1000 to a double at an interest rate of 7.2% for each compounding period
a) annually
b) semi-annually
c) monthly
d) daily

Please Show Full Solutions .. thank you

Answer 1

after each period you get the ammount that you already had + 7.2% of that ammount.
1000 + 1000 (7.2/100)
= 1000 + 1000 (72/1000)
= 1000 + 72
= 1072.

Next year you add 7.2% of 1072 to 1072.
For semi-anual calculation, you can devide 7.2% by 2

Answer 2

1.072 t = ln2
-> t = ln2/ 1.072 = .65 ( ~ 1 yr)

Answer 3

2. 072 t = ln2
=>t = ln2/ 2.072 = .33 yr

Answer 4

-> t = ln2/ 12.072 = .06 yr

Answer 5

-> t = ln(2)/ 365.072 = .002 yr