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Natasha2012 [34]
3 years ago
5

Lisa Richter deposited $5,000 at 4% compounded semiannually for three years. At the beginning of the fourth year, Lisa deposited

$2500 What would her balance earning 4% compounded semiannually?
a) $8,78726
b) $8,801.05
c) $8,800
d) $8,424
Business
1 answer:
Contact [7]3 years ago
7 0

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

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