Question

Find the maturity value of ₱10,000 is deposited in a bank at 2% compounded quarterly for 5 years?​

Answer 1

Step-by-step explanation:

Chapter 4 Class Handout

Simple Interest: A = P(1+rt)

P: the principal, the amount invested

A: the new balance

t: the time

r: the rate, (in decimal form)

Ex1: If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.

P = $1000, t = 2 years, r = 0.08.

A = 1000(1+0.08(2)) = 1000(1.16) = 1160

Compound Interest:

P: the principal, amount invested

A: the new balance

t: the time

r: the rate, (in decimal form)

n: the number of times it is compounded.

Ex2:Suppose that $5000 is deposited in a saving account at the rate of 6% per year. Find the total amount on deposit at the end of 4 years if the interest is:

P =$5000, r = 6% , t = 4 years

a) simple : A = P(1+rt)

A = 5000(1+(0.06)(4)) = 5000(1.24) = $6200

b) compounded annually, n = 1:

A = 5000(1 + 0.06/1)(1)(4) = 5000(1.06)(4) = $6312.38

c) compounded semiannually, n =2:

A = 5000(1 + 0.06/2)(2)(4) = 5000(1.03)(8) = $6333.85

d) compounded quarterly, n = 4:

A = 5000(1 + 0.06/4)(4)(4) = 5000(1.015)(16) = $6344.93

e) compounded monthly, n =12:

A = 5000(1 + 0.06/12)(12)(4) = 5000(1.005)(48) = $6352.44

f) compounded daily, n =365:

A = 5000(1 + 0.06/365)(365)(4) = 5000(1.00016)(1460) = $6356.12

Continuous Compound Interest:

Continuous compounding means compound every instant, consider investment of 1$ for 1 year at 100% interest rate. If the interest rate is compounded n times per year, the compounded amount as we saw before is given by: A = P(1+ r/n)nt

the following table shows the compound interest that results as the number of compounding periods increases:

P = $1; r = 100% = 1; t = 1 year

Compounded Number of periods per year Compound amount

annually 1 (1+1/1)1 = $2

monthly 12 (1+1/12)12 = $2.6130

daily 360 (1+1/360)360 = $2.7145

hourly 8640 (1+1/8640)8640 = $2.71812

each minute 518,400 (1+1/518,400)518,400= $2.71827

As the table shows, as n increases in size, the limiting value of A is the special number

e = 2.71828

Answer 2

Given: ₱10,000 is deposited in a bank at 2% compounded quarterly for 5 years.

To find: Maturity value of the money deposited

Solution: The principal is the sum of money that is deposited in the bank.

Let the principal be denoted by p, rate be r, amount be a and time be denoted by t.

p= ₱10,000

A quarter year is equal to the 1/4 of a year.

Therefore,

time (t)= 5 years

= 5×4 quarter years

= 20 quarter years

Rate(r) = 2%

= (2/4)% quarterly

= 0.5 % quarterly

Maturity value is equal to the amount that is received at the end of 5 years.

The value for amount when principal is compounded quarterly is given by the formula:

$a = p {(1 + \frac{r}{100}) }^{t}$

$= > a = 10000 {(1 + \frac{0.5}{100}) }^{20}$

$= > a = 10000 {( \frac{100.5}{100}) }^{20}$

$= > a = 10000 \times ( {1.005)}^{20}$

$= > a = 10000 \times 1.105$

$= > a = 11050$

Therefore, the maturity value of the money invested is ₱11,050.