Question

On January 1st, 2020, an investment portfolio was valued at $10,000. Due to COVID-19 concerns, world markets plummetted in value in early 2020, and as of April 1st, 2020 the portfolio had a value which was only 75% of its value at the beginning of the year. Stock markets have proven to be resilient over time, so assuming that markets recover at an annual rate of 5.5% compounded quarterly, how long will it take for the portfolio to recover to its January 1st, 2020 value? Express your answer in years rounded to one decimal point.

Answer 1

Investment Portfolio on 1st Jan, 2020 = $10000

Investment Portfolio on 1st April 2020 = 75% of $10000

= $7500

Recovering Rate (r) = 5.5% compounded quarterly

So, now we have to recover the portfolio to $10000 and decide how many years are going to make it to $10000.

Future Amount = Present Amount × (1 + recovering rate/100)number of years

Here, Recovering rate is compounded quarterly so r = 5.5/4

$10000 = $7500×(1+5.5/400)n

1.3333 = (405.5/400)n

1.3333 = 1.01375n

Taking log both sides

Log(1.3333) = n × log(1.01375)

0.1249 = n × 0.0059

Therefore,

n = 0.1249/0.0059

n = 21.16

Now we have to divide n by 4 because of quarterly compound to get number of years.

Number of Years = 21.16/4

= 5.3 (approx)

So, it will take 5.3 years to recover portfolio.