An investment of ₱260,200 at the rate of 4.5% per annum, compounded quarterly, will reach approximately around ₱292,800 in close to:

Question

An investment of ₱260,200 at the rate of 4.5% per annum, compounded quarterly, will reach approximately around ₱292,800 in close to:

Answer 1

Use the general formula:

A=P(1+r/n)^nt where

P = intial investment

A = Amount after t years a r interest, compounded n times per year

r= annual interest rate

n= number of compounding periods per year

t = number of years

292.8 = 260.2(1+ 0.045/4)^4t

solve for t

use a calculator

(1.01125)^4t = 292.8/260.2 = 1.12528824

4t = log_1.011251.12528824

4t = ln1.12528824/ln1.01125 = .1180392162/.0111871871871894

= 10.55128434

t= 10.55128434/4

= 2.637821084 years

check the answer, see if it's close to continous compounding

it should be slightly longer. continuous slightly less than 1/4ly

A=Pe^rt

292.8 = 260.2e^.045t

292.8/260.2 = e^.045t

.045t = ln(292.8/260.2)

t = 2.623093693 years= nearly the same as 2.637821084

2.627821084 years

= about 2 years and 229 days

= about 2 year and 7 1/2 months