A person invested $7,400 in an account growing at a rate allowing the money to

Mathematics

1 answer:

Tema [17]3 years ago

6 0

Answer:

$13,304

Step-by-step explanation:

-We use the compound interest function to determine the rate of growth.

-Given that the amount doubles in 13 years, the annual growth rate is calculated as:

$A=P(1+i)^n\\\\2P=P(1+i)^n\\\\\therefore 2=(1+i)^{13}\\\\i=2^{1/13}-1=0.05477$

We now substitute this value of i in the compound interest formula equation to solve for future value:

$A=P(1+i)^n\\\\\\=7400(1.05477)^{11}\\\\\\=13303.54$

$\approx13304$

Hence, the future value to the nearest dollar is $13,304

*You can alternatively use the exponential growth function:

$P_t=P_oe^{rt}\\\\2=e^{13r}\\\\r=\frac{In \ 2}{13}=0.05332\\\\\therefore P_{11}=7400e^{0.05332\times 11}\\\\=13303.14$

This is slightly off by just $1

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