Question

Lisa Richter deposited $5,000 at 4% compounded semiannually for three years. At the beginning of the fourth year, Lisa deposited $2,500. What would her balance be at the end of five years assuming she is still earning 4% compounded semiannually?

Answer 1

formula for compound interest is P(1+(r/n))^nt
P=principle (5000)
r=rate (4% or 0.04)
n= number of times compounded (semi annually 2 times)
t= time (3 years)
$8130.81 after the 2500 deposit
at the end of the fifth year $8459.29

Answer 2

$8,801.05

Explanation:

Lisa Richter deposited $5,000 at 4% compounded semiannually for three years.

To calculate the amount after 3 years we use the formula

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

Where A = Future amount

P = Principal amount ($5,000)

r = rate of interest 4% (0.04)

n = number of compounding interest semiannually (2)

t = time (3 years)

Now put the values in the formula

`A=5000(1+(0.04)/(2))^((2)(3))`

`A=5000(1+0.02)^((2)(3))`

`A=5000(1.02)^((6))`

A = 5000(1.126)

A = $5,630.81

At the beginning of the fourth year Lisa deposited $2,500. Now the amount would be

New principal amount = 5630.81 + 2500 = 8,130.81

we have to calculate the future amount at the end of five years or for 2 more years.

We will use the same method as we done above.

`A=8130.81(1+(0.04)/(2))^((2)(2))`

`A=8130.81(1+0.02)^((4))`

`A=8130.81(1.02)^((4))`

A = 8130.81 (1.08243)

A = $8,801.05

Lisa's balance at the end of five years $8,801.05