Question

Financial Math

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compound quarterly. If she spent $7,400, how much total will she have paid after 8 years

a.) $15,927.56

b.) $16,109.05

c.) 15,683.28

d.) $15,415.94

Answer 1

C

Explanation:

Answer 2

Option C

Olivia paid $ 15683.28 after 8 years

Solution:

Given that Olivia decides to buy the furniture on credit with 9.5% interest compound quarterly

She spent $ 7400

To find: total amount paid after 8 years

The formula for amount using compound interest is given as:

`A=p\left(1+(r)/(n)\right)^(n t)`

Where,

"p" is the principal amount

"r" is the annual interest rate in decimal

"t" is the time the money is invested or borrowed for

"n" is the number of times that interest is compounded per unit t

Here in this problem,

p = $ 7400

`r = 9.5 \% = (9.5)/(100)`

t = 8 years

n = 4 (since interest is compounded quartely)

Substituting the values in given formula,

`A=7400\left(1+(9.5)/(100 * 4)\right)^(4 * 8)`

`A=7400(1+0.02375)^(32)`

`A=7400(1.02375)^(32)`

`\begin{array}{l}{A=7400 * 2.11936263142} \\\\ {A=15683.28}\end{array}`

Thus the total amount she paid after 8 years is $ 15,683.28