Question

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​

Answer 1

Refer to the attachment

Answer 2

Answer:

${ \underline{ \mathfrak{ \: asnwer : }}}$

Richard's investment = David's investment

• From compound interest formula:

${ \boxed{ \bf{investment = p(1 + \frac{r}{100}) {}^{n} }}}$

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

Therefore:

${ \rm{10000(1 + \frac{x}{100}) {}^{7} = 10000(1 + \frac{2}{100}) { }^{7} }} \\ \\ { \rm{1 + \frac{x}{100} = 1 + \frac{2}{100} }} \\ \\ { \rm{x = \frac{2 \times 100}{100} }} \\ \\ { \boxed{ \rm{ \: x = 2 \: }}}$