What is the value of the cd after 3 years?

Question

If you invest ₱5,000 in a certificate of deposit (CD) with 2.5% interest compounded quarterly for 3 years. Determine the value of the CD after 3 years.

The accumulated amount, A, in a compound interest account can be determined using the formula:

A(t)=P₀(1+ r/n)^nt

show solution

Answer 1

Hi Jeon A

For

A(t)=P₀(1+ r/n)^nt

You just need to assign your values and plug them into the formula

A = Balance after 3 years

P₀ = Initial investment $5000

r = your rate written as a decimal 0.025

n = number of compounding periods, yours is quarterly so you have 4

t = number of years

So you have

A(t) = 5000( 1 + (0.025/4))^4*3

A(t) = 5000(1 + 0.00625)¹²

A(t) = 5000(1.00625)¹²

A(t) = 5000(1.0776) = 5388 to the nearest dollar.

You can check this by calculating the interest then adding it to the principal

C = P((1+ r)¹² - 1)

C = Your total compounded interest

P = Your starting Principal

r = interest per period = 0.025/4 because your have quarterly compounding periods

n = total number of periods = 3years x 4 periods so in three years you have a total 12 periods

C = P((1+ r)¹² - 1) =5000((1+.025/4)¹² - 1) = 388 to the nearest dollar

C = 5000((1.00625)¹² - 1))

C = 5000(1.0776 -1)

C = 5000(.0776) = 388

P + C = A = 5000 + 388 = 5388.

While these may not be the exact equations referred to in your text, you can look the many forms on the internet. I hope this helps

Answer 2

Compound Interest formula:

A_(t)=P₀(1+ r/n)^nt

Where:

A(t): balance in the account after t years

P₀: starting balance, initial deposit

r: interest rate in decimals

n: number of compounding periods in one year

t: number of years

In this case:

A_(t) = A₍₃₎

P₀ = 5000

r = 0.025

n: 4

t = 3

A₍₃₎ = 5000 (1 + 0.025/4)⁽⁴⁾⁽³⁾

A₍₃₎ = 5000 (1 + 0.00625)¹²

A₍₃₎ = 5000 (1.00625)¹²

A₍₃₎ = 5000 (1.0778)

A₍₃₎ = 5388.17

The value of the CD after 3 years is $5388.17