Question

50 POINTS!
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Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.7%. She made no other deposits or withdrawals and the total amount in her account after 15 years was $12,158.10. How much did she deposit?

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Answer 1

$7,015.11

• total money accrued : $12,158.10

• years :  15 years

• rate of interest : 3.7%

• deposited : A

Depth meanings:

• P is deposited money

• semiannually : 2 times in a year

• A is received or acquired money

• t is time in years

• r is rate in percentage

$\sf P = \dfrac{A} { (1 + \dfrac{r}{n})^{nt}}$

$\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}$

$\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}$

$\rightarrow \sf P = 7015.113646$