SOLUTION: 1. Sajid has a goal of saving $20 000 in 8 years. What principal invested for 5 years at 6% per annum, compounded semi-annually, then for the next 3 years at 6.5%/a, compounded qua

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 1. Sajid has a goal of saving $20 000 in 8 years. What principal invested for 5 years at 6% per annum, compounded semi-annually, then for the next 3 years at 6.5%/a, compounded qua      Log On

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Question 241324: 1. Sajid has a goal of saving $20 000 in 8 years. What principal invested for 5 years at 6% per annum, compounded semi-annually, then for the next 3 years at 6.5%/a, compounded quarterly, would achieve this goal?


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula is
A=+P%2A%281+%2B+r%2Fn%29%5E%28nt%29
For 5 year investment:
t+=+5 yrs
n+=+2 (semi-annually)
r+=+.06
A%5B5%5D+=+P%5B5%5D%2A%281+%2B+.06%2F2%29%5E%282%2A5%29
A%5B5%5D+=+P%5B5%5D%2A1.03%5E10
A%5B5%5D+=+1.3439P%5B5%5D
------------------------
For 3 year investment:
t+=+3
n+=+4 (quarterly)
r+=+.065
A%5B3%5D+=+P%5B3%5D%2A%281+%2B+.065%2F4%29%5E%284%2A3%29
A%5B3%5D+=+P%5B3%5D%2A%281+%2B+.01625%29%5E12
A%5B3%5D+=+P%5B3%5D%2A1.01625%5E12
A%5B3%5D+=+1.2134P%5B3%5D
------------------------------
If I read the problem right, A%5B5%5D, the earnings
after 5 years, will become P%5B3%5D, the principle
invested for 3 years
given:
A%5B5%5D+=+P%5B3%5D
A%5B3%5D+=+20000
--------------------
substituting:
A%5B3%5D+=+1.2134P%5B3%5D
20000+=+1.2134P%5B3%5D
P%5B3%5D+=+16482.61
and
A%5B5%5D+=+P%5B3%5D
A%5B5%5D+=+16482.61
A%5B5%5D+=+1.3439P%5B5%5D
16482.61+=+1.3439P%5B5%5D
P%5B5%5D+=+12264.76
The original principle invested is $12,264.76
Hope I got it right