Question

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

Answer 1

Interest earned = $3546.50

Option B is correct option.

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+(r)/(n))^(nt)`

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

`A=P(1+(r)/(n))^(nt)\\A=3815.24(1+(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.