Nichols Electric expects to replace a 500000 piece of equipm

Nichols Electric expects to replace a $500,000 piece of equipment in 4 years. It plans to accumulate the necessary funds by making equal monthly deposits into a bank fund that earns 3/4% per month. What is the monthly deposit? Draw a CFD. (Answer: $8700)

Solution

The formula applicable here is A = P [ [(1+r)ⁿ -1] (1+r)/r where P is the monthly instalment, r is the rate of interest per period in decimals, n is the number of periods and A is the target amount. Here, A = 500000, r = 0.75/100 = 0.0075, n = 4*12 = 48. Then 500000 = P [ (1.0075)⁴⁸ -1](1.0075/0.0075) or, P = [500000*0.0075/1.0075]/ ( 1.431405333-1) = 3722.084367/0.431405333 = $ 8627.81 ( on roundin off to the nearest cent). In case $ 8700 are deposied per month , the future value will be 500000*8700/8627.81 = 504183.56. Then Nicholas Electic will get an additional amount of $ 4183.56 ( in addition to the target amount of $ 500000).