Question

Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. Using the tables in the Business Math Handbook that accompanies the course textbook, determine which one of the following is the best deal.
A. Mystic for last two years
B. Mystic
C. Four Rivers
D. Four Rivers for first two years

Answer 1

Answer:

The answer is option (C). Four Rivers Bank

Explanation:

a). The total amount Jane will receive after 5 years after investing $40,000 in the Mystic Bank can be expressed 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=$40,000

r=12/100=0.12

n=interest is compounded quarterly which is four times a year=4

t=5 years

Replacing values in the formula;

A=40,000(1+0.12/4)^(4×5)

A=40,000(1+0.03)^20

A=40,000×1.806

A=72,244.45

The total amount Jane will receive after 5 years if she chooses to invest with the Mystic Bank is $72,244.45

b). The total amount Jane will receive after 5 years after investing $40,000 in the Four Rivers Bank can be expressed as follows;

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

where;

P=$40,000

r=14/100=0.14

n=interest is compounded semiannually which is two times a year=2

t=5 years

Replacing values in the formula;

A=40,000(1+0.14/2)^(2×5)

A=40,000(1+0.07)^10

A=40,000×1.967

A=78,686.05

The total amount Jane will receive after 5 years if she chooses to invest with the Four Rivers Bank is $78,686.05

c). The best deal would be to invest with Four Rivers Bank for 5 years since the total amount Jane will receive after 5 years will be $78,686.05 which is greater than $72,244.45, which is the total amount she will receive if she chooses to invest with Mystic Bank