Answer:
Answer is option (d) $8,424
Explanation:
The total amount Lisa Richter will receive after the end of the first 3 years can be expressed using the formula for calculating the total amount after 3 years with interest compounded semiannually is as follows;
A = P (1 + r/n)^(nt)
where;
A = the future value of the initial investment
P = initial investment amount/principal amount
r = the annual interest rate
n = the number of times that interest is compounded per unit t
t = the time the money is invested for
In our case;
P=$5,000
r=4/100=0.04
n=interest is compounded semiannually which is twice a year=2
t=3 years
Replacing values in the formula;
A=5,000(1+0.04/2)^(2×3)
A=5,000(1+0.02)^6
A=5,000(1.02)^6
A=$5,630.81
Total amount after the end of the first 3 years=$5,630.81
To calculate the total principal amount for the fourth year;
Total principal amount=Total amount after 3 years+Amount deposited at the beginning of the fourth year
where;
Total amount after 3 years=$5,630.81
Amount deposited at the beginning of the fourth year=$2500
replacing;
Total principal amount=(5,630.81+2500)=8,130.81
Using the formula;
A = P (1 + r/n)^(nt)
P=$8,130.81
r=4/100=0.04
n=compounded semiannually=2
t=1 year
replacing;
A=8,130.81(1+0.04/2)^(2×1)
A=8,130.81(1.02)^2
A=8,459.29
Option (d) $8,424 is closer to 8,459.29, take answer as (d) $8,424
