Question

An investor opened a saving account with $K earning simple interest rate at a rate of 2.5% annually. Four years later, the investor closed the account and invested the accumulated amount in a saving account earning 5% compound interest. Determine the number of years necessary for the balance to reach $3K.

Answer 1

Amount invested = $K

Amount at simple interest after 4 years = K + Krt/100 = K + K*2.5*4/100 = 1.1K

Let the number of years for the amount to reach 3K be n

=> 1.1K(1+2.5/100)ⁿ = 3K

=> 1.025ⁿ = 2.73

=> n ln(1.025) = ln(2.73)

=> n = 40.63

Hence, the amount becomes 3K after 40.63 years