Mathematics: Lucas opened a savings account 20 years ago with a deposit of $3,815.24. The account has an interest rate of 3.3% compounded quarterly. How much interest has Lucas earned? a. $3,488.21 b. $3,546.50 c. $3,815.24 d. $3,941.14

1st-3rd-2nd-4th-1stStep-by-step explanation:...

Lucas opened a savings account 20 years ago with a

Ответ:

jgill27

13.02.2022

Mathematics

Interest earned = $3546.50

Option B is correct option.

Step-by-step explanation:

Time t = 20 years

Principal Amount P =$3815.24

Interest r = 3.3% or 0.033

Compounded quarterly n = 4

We need to find How much interest has Lucas earned?

First we need to find the future value in the account after 20 years

The formula used to find future value A is: $A=P(1+\frac{r}{n})^{nt}$

Putting values of t, r , n and P to find A i.e future value

$A=P(1+\frac{r}{n})^{nt}\\A=3815.24(1+\frac{0.033}{4})^{20*4} \\Simplifying:\\A=3815.24(1+0.00825)^{20*4} \\A=3815.24(1.00825)^{80}\\A=3815.24(1.929)\\A= 7361.74$

Now finding interest amount by subtracting the initial deposit from the future value

Interest earned = Future Value (A)- Initial Deposit (P)

Interest earned = 7,361.74 - 3815.24

Interest earned = 3546.50

So, Lucas have earned interest = $3546.50

Option B is correct option.

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Lucas opened a savings account 20 years ago with a deposit of $3,815.24. The account has an interest rate of 3.3% compounded quarterly. How much interest has Lucas earned?
a. $3,488.21
b. $3,546.50
c. $3,815.24
d. $3,941.14

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