Bank A is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank B, her $2,000 will grow to $3,700.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest = [tex]\frac{Principal * Rate * Time}{100}[/tex]
What is compound interest?
Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
[tex]A = P (1+\frac{r}{100} )^{t}[/tex]
where,
A = final amount
P = initial amount
r = rate per annum
t = time in years
According to the question
Anastasia was trying to decide which investment plan would be best over 10 years
Bank A:
Simple interest
Principal = $2,000
Rate per annum = 8.5%
Time in years = 10 years
Now , using simple interest formula
Simple interest = [tex]\frac{Principal * Rate * Time}{100}[/tex]
Simple interest = [tex]\frac{ 2000 * 8.5 * 10 }{100}[/tex]
= 1700
Total Amount after 10 years = $2,000 + $ 1700
= $3700
Bank B:
Compound Interest
Rate per annum = 8%
Time in years = 10
Principal = $2,000
Now,
Applying compound interest formula
[tex]A = P (1+\frac{r}{100} )^{t}[/tex]
[tex]A = 2000 (1+\frac{8}{100} )^{10}[/tex]
[tex]A = 2000 (1.08} )^{10}[/tex]
A = 4,317.85
Hence, Bank A is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank B, her $2,000 will grow to $3,700.
To know more about compound interest and simple interest here:
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