Answer to Question #265414 in Financial Math for piumini Ireshika

Question

1. Find the time required for $200 to grow to $600 if interest rate is 8.5% p.a. compounded annually. (Round the answer to the nearest month)
2. Find the accumulate amount of $1000 at the end of year 5 if interest is

• 8% p.a. for the first year
• 8.5% p.a. for the second year
• 9% p.a. for the third and fourth year
• 8% p.a. in the fifth year

1. David deposits $10,000 into his savings account that earns interest at 9% p.a. compounded annually for the first 2 years, 8% p.a. compounded semi-annually for the next 3 years and 12% p.a. compounded monthly for the next 2 years. Find the accumulated amount at the end of 7 years.
2. Find the accumulate amount if (a) $300 is invested at 5.5% p.a. compounded yearly for 3 years? (b) $500 is invested at 7% p.a. compounded quarterly for 4 years? (c) $700 is invested at 12% p.a. compounded monthly for 6 years? (d) $8400 is invested at 4% p.a. compounded quarterly for 5 years?

Answer 1

1.

Compounded annually

Pn = P(1 + r)^t – P

Given; r = 8.5% p.a.

p = $200

Pn = $600

Thus, 600 = 200(1+0.085)^t - 200

(600-200)=200(1+0.085)^t

400=200(1+0.085)^t

200=(1+0.085)^t

200=1.085^t

Log200 = t Log(1.085)

2.3011= 0.03543t

t=6.5years

2.

For the first year

Simple interest= Principle*Rate*Time

SI=1000*0.08*1

=80+1000

=1080

For the second year

A=P*R*T

1080*0.085*2

=183.6+1080

=1263.6

For the third year

1263.6*0.09*3

=341.17+1263.6

=1604.77

Fourth year

1604.77*0.09*4

=577.72

=2182.45

In the fifth year

2182.45*0.08*5

=872.995

=872.995+2182.45

=3055.45

1)

Compounded annually

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

=10,000{1+(0.09/1)²

=$11881

Compounded semi-annually for the next 3 years

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

=10000{1+(0.09/2)⁶

=$13022.60

12% p.a. compounded monthly for the next 2 years.

n=12

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

10000(1+0.01)²⁴

=$12697.35

Accumulated amount at the end of 7 years

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

A=10000(1+0.09)⁷

=$18280.39

2)

(a)Compounded Yearly for 3years

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

A=300(1+0.055)³

=$352.27

b)Compounded quarterly for 4 years

n=4

A=500{1+(0.07/4)}¹⁶

=$659.96

c)Compounded monthly

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

A=700(1+0.12)⁶

$1381.68

d)Compounded quarterly for 5 years

n=4

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

8400{1+(0.04/4)²⁰

=$10249.60