Question

You need to have $20,000 for a down payment on a house 6 in years. If you can earn an annual interest rate of 4.2 percent, how much will you have to deposit today?

Answer 1

Answer: you have to deposit $15625 today

Step-by-step explanation:

Assuming the interest is compounded annually. 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

From the information given,

A = $20000

r = 4.2% = 4.2/100 = 0.042

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

t = 6 years

Therefore,.

20000 = P(1 + 0.042/1)^1 × 6

20000 = P(1.042)^6

20000 = 1.28P

P = 20000/1.28

P = $15625