Please solve the following questions on compound interest?

(a) How much an investment of #€5000# will become in #7# years if compounded every quarter at #4.5%# per annum?
(b) Carla invested #$7000# compounded annually and it doubled in #10# years. What is the rate of interest (up to #2dp#)?

1 Answer
Nov 9, 2017

(a) #€6847.26# and (b) #7.18%# per annum

Explanation:

A principal amount of #P# invested for #t# years at #r%# annual interest rate compounded #n# times a year at equal intervals becomes

#P(1+(r/n)/100)^(nt)# or #P(1+r/(100n))^(nt)#

The reason for this is follows. Suppose interest is compounded quarterly i.e. #4# times a year, then interest at the end of each quarter will be #Pxxr/400# and amount will grow to #P(1+r/400)# and after #t# years or #4t# quarters, it will become #P(1+r/400)^(4t)#.

(a) Here interest rate is #4.5%# annual and as we are compounding monthly, at each month it is #4.5/12%# or #3/8%#. Further there are #7xx12=84# months in #7# years. So the investment of #€5000# becomes

#5000(1+3/800)^84=5000xx1.00375^84#

= #5000xx1.36945226=6847.2613~=€6847.26#

(b) As Carla has invested #$7000# compounded annually for #10# years at say #r%# per annum and amount doubles, we have

#7000(1+r/100)^10=14000#

or #(1+r/100)^10=2#

or #1+r/100=2^(1/10)=2^0.1=1.0717735#

or #r/100=0.071773#

or #r=7.1773%~=7.18%#