Question

Thirteen semi-annual deposits are made earning interest of 6.3​% compounded semi-annually. The size of the first deposit is $1600 and the deposits increase at 3.2​% thereafter.

a)Determine the total amount deposited

b)how much was the accumulated value of the deposits just after the last deposits was made

c)what is the size of the 11th deposits

d)what is the amount of interest included in the accumulated value

Answer 1

a) The total amount deposited here is computed as the sum of the geometric progression with first term as the first deposit amount of 1600, common ratio as (1.032) as 3.2% is the increase rate and total number of terms as n = 13. Therefore the total sum deposited here is computed as:

Therefore 25301.92 dollars is the total amount deposited here.

b) The accumulated value just after the last deposit is computed here as:

This is a sum of a geometric progression with common ratio as: r = 1.032 / 1.0315

Therefore 30266.18 dollars is the required accumulated value here

c) The size of the 11th deposit is computed here as:

= 1600*(1.032)10 = 2192.39

Therefore 2192.39 dollars is the required deposit value here.

d) The amount of interest accumulated is computed here as:

= Total accumulated value of all deposits - Total value of all deposits

= 30266.18 - 25301.92

= 4964.26

Therefore 4964.26 is the required value of interest here.