Question

On the day that Ramon is born, his grandfather deposited $5000 for him in a certificate of deposit paying 10% interest compounded annually. When Ramon is old enough to manage the account himself, he decides that he will not withdraw the money until the certificate is worth $1,000,000.
How old will he be when the account reaches this amount?

Answer 1

The time required to get a total amount of $1,000,000.00 with compounded interest on a principal of $5,000.00 at an interest rate of 10% per year and compounded 1 times per year is 55.59 years.

Given data

Principal = $5,000

Rate = 10%

Final Amount A= $1,000,000

Time = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(1,000,000.00/5,000.00) / ( 1 × [ln(1 + 0.1/1)] )

t = ln(1,000,000.00/5,000.00) / ( 1 × [ln(1 + 0.1)] )

t = 55.59 years

(about 55 years 7 months)

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