Question

Consider the function y = 1.05(x/12), which represents the growth of capital in a bank account.

The annual interest is __%,
a. 12
b. 105
c. 1.05
d. 5
and the bank compounds the interest__ .
a. annually
b. continuously
c. daily
d. monthly

The balance of the account will grow __ .
a. logarithmically
b. exponentially
c. asymptotically
d. linearly

Answer 1

1) is A
2) is D
3)is D

Answer 2

The annual interest is,

Option d is correct

5%

The bank compounds the interest_

Option a is correct.

Annually.

The balance of the account will grow,

Option b is correct

exponentially

Explanation:

Exponential growth function is given by:

`y=(1+r)^x` .....[1]

where,

r is the annual interest in decimal

x is the number of periods.

As per the statement:

Consider the function:

`y=(1.05)^{(x)/(12)}` where, x represents the time in months.

On comparing with [1] we have;

`1+r = 1.05`

Subtract 1 from both sides we have;

r = 0.05 = 5%

The annual interest is, 5%

and

the bank compounds the interest annually.

The balance of the account will grow exponentially