Question

Suppose you deposit $1,000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn from the account, answer the following questions.

a. How much will be in the account after 4 years?
b. How much will be in the account after 18 years?
c. How many years will it take for the account to contain $1,500?
d. How many years will it take for the account to contain $2,000?

Answer 1

Explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

a) From the information given,

P = $1000

r = 4% = 4/100 = 0.04

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,

A = 1000(1 + 0.04/1)^1 × 4

A = 1000(1.04)^4

A = $1170

b) After 18 years, t = 18, therefore

A = 1000(1.04)^18

A = $2026

c) When A = $1500, then

1500 = 1000(1.04)^t

1500/1000 = (1.04)^t

1.5 = (1.04)^t

Taking log of both sides, it becomes

Log 1.5 = tlog(1.04)

0.176 = 0.017t

t = 0.176/0.017

t = 10.35 years

d) When A = $2000, then

2000 = 1000(1.04)^t

2000/1000 = (1.04)^t

2 = (1.04)^t

Taking log of both sides, it becomes

Log 2 = tlog(1.04)

0.301 = 0.017t

t = 0.301/0.017

t = 17.7 years