Question 241324
The formula is
{{{A= P*(1 + r/n)^(nt)}}}
For 5 year investment:
{{{t = 5}}} yrs
{{{n = 2}}} (semi-annually)
{{{r = .06}}}
{{{A[5] = P[5]*(1 + .06/2)^(2*5)}}}
{{{A[5] = P[5]*1.03^10}}}
{{{A[5] = 1.3439P[5]}}}
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For 3 year investment:
{{{t = 3}}}
{{{n = 4}}} (quarterly)
{{{r = .065}}}
{{{A[3] = P[3]*(1 + .065/4)^(4*3)}}}
{{{A[3] = P[3]*(1 + .01625)^12}}}
{{{A[3] = P[3]*1.01625^12}}}
{{{A[3] = 1.2134P[3]}}}
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If I read the problem right, {{{A[5]}}}, the earnings
after 5 years, will become {{{P[3]}}}, the principle
invested for 3 years
given:
{{{A[5] = P[3]}}}
{{{A[3] = 20000}}}
--------------------
substituting:
{{{A[3] = 1.2134P[3]}}}

{{{20000 = 1.2134P[3]}}}
{{{P[3] = 16482.61}}}
and
{{{A[5] = P[3]}}}
{{{A[5] = 16482.61}}}
{{{A[5] = 1.3439P[5]}}}
{{{16482.61 = 1.3439P[5]}}}
{{{P[5] = 12264.76}}}
The original principle invested is $12,264.76
Hope I got it right