Question

Calculate the future value in four years of $7,000 received today if your investments pay (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) Future Value a. 5 percent compounded annually $ b. 7 percent compounded annually c. 9 percent compounded annually d. 9 percent compounded semiannually e. 9 percent compounded quarterly

Answer 1

The formula for Future Value at compound interest is: Amount= P(1+ r)ⁿ

Where P is the principal in Year 0,

r is the rate of interest expressed as a decimal,

n is number of periods.

The important point to be noted is that: if compounded semiannually, r is divided by 2 and n is multiplied by 2.

a.

P=$ 7000

n=4

r=5% compounded annually ,so r=.05

So, Amount=7000(1+.05)⁴ =7000(1.05)⁴= 7000(1.21551) =$8508.54

b.

r= 7% compounded annually, r=.07, n=4

So, Amount=$7000(1+.07)⁴= 7000(1.3108)= $9175.57

c.

9% compounded annually. Therefore, r=.09, n=4

So, Amount =$7000(1+.09)⁴=7000(1.41158) = $9881.07

Answer: $9881.07

d.

9% compounded semi-annually

So, r=.09/2= .045

n=4x2= 8 periods

Amount=$7000(1+.045)⁸ = $7000(1.4221) = $9954.70

Answer: $ 9954.70

e.

9% compounded quarterly

So, r = .09/4 = .0225 (since there are 4 quarters in a year)

n= 4x4 = 16 periods

Therefore, Amount=$7000(1+ .0225)¹⁶=$7000(1.0225)¹⁶= $7000(1.42762) = $ 9993.35

Answer: $9993.35