Question

900.00 deposit in the bank earning 3% interest how long will it take to earn $135.00 dollars?

Answer 1

`color(maroon)("It will take 5 years to earn $ 135 with Simple Interest"`

`color(chocolate)("It will take 4.73 years to earn $ 135 with Compound Interest"`

Explanation:

Case : 1 - Assuming it to be simple interest

`I = (P N R) / 100`

`I = $ 135, P = $ 900, R = 3%, N = ?`

`N = (100 * I ) / ( P * R) = (100 * 135) / (900 * 3) = 5 years`

Case : 2 - Assuming it to be Compound Interest.

`P + I = P (1 + R/100)^N`

`900 + 135 = 900 (1 + 3/100)^N`

`1.03^N = 1035 / 900 = 23/20 = 1.15`

#N log 1.03 = log 1.153

`N = log 1.15 / log 1.03 ~~ 4.73 years`