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6) Richard and David both invest $10 000. Richard invests his $10,000 at a rate of x% compound interest per year. David invests his $10,000 in a bank that pays 2% simple interest per year. After 7 years, their investment is worth the same amount. Calculate the value of x​

Sagot :

Refer to the attachment

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Answer:

[tex]{ \underline{ \mathfrak{ \: asnwer : }}}[/tex]

Richard's investment = David's investment

• From compound interest formula:

[tex]{ \boxed{ \bf{investment = p(1 + \frac{r}{100}) {}^{n} }}}[/tex]

  • P is the principle
  • r is the rate
  • n is the period

Therefore:

[tex]{ \rm{10000(1 + \frac{x}{100}) {}^{7} = 10000(1 + \frac{2}{100}) { }^{7} }} \\ \\ { \rm{1 + \frac{x}{100} = 1 + \frac{2}{100} }} \\ \\ { \rm{x = \frac{2 \times 100}{100} }} \\ \\ { \boxed{ \rm{ \: x = 2 \: }}}[/tex]

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