Question

Suppose you are committed to owning a $200,000 Ferrari. If you believe your mutual fund can achieve an annual return of 10.65 percent, and you want to buy the car in 11 years on the day you turn 30, how much must you invest today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Amount to be invested $

Answer 1

Answer: Amount to be invested is

$6564.10

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

From the information given,

A = 200000

r = 10.65% = 10.65/100 = 0.1065

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

t = 11 year

Therefore,.

200000 = P(1+0.10659/1)^1 × 11

200000 = P(1.10659)^11

P = 200000/(1.10659)^11

P = $6564.10