Question

Question 75 ptsNeeki's parents gave her some money as a gift and she deposit all of it in a bankthat pays 6% annual interest compounded quarterly. After 15 years her balanceis $21,000.How much money as a gift her parents gave him.Use six digits after decimal when calculating.For your final answer, round to two digits after decimal.Select the closest answer

Answer 1

$8,595.21

Step-by-step explanation

The compound interest formula is,

`A=P\left(1+(r)/(n)\right)^(nt)`

Where P is the deposited amount, r is the interest rate, n is the number of times the interest is compounded per year, t is the time in years, and A is the balance after t years.

We have to find P, so we have to solve the equation above for P,

`P=(A)/(\left(1+(r)/(n)\right)^(nt))`

We have that:

• A = $21,000

,

• r = 0.06

,

• n = 4 (the interest is compounded quarterly)

,

• t = 15 years

Replace the known values and solve,

`P=(21,000)/(\left(1+(0.06)/(4)\right)^(4\cdot15))=(21,000)/((1+0.015)^(60))=(21,000)/(1.015^(60))=(21,000)/(2.443220)\approx8595.21`

Hence, her parents gave her $8,595.21.