Question

Find the accumulated value of $18,000 invested for 8 years:

(A) at a nominal annual rate of interest of 4.5% convertible quarterly.

(B) at 4% per year compounded weekly.

(C) at a discount rate of 2.8% per year compounded monthly.

Answer 1

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $18000, r = rate of interest, n= time period

(A) 4.5 % Converted quarterly:

Given: r = rate of interest = 4.5% converted quarterly, so quarterly rate = 4.5% / 4 = 1.125%,  n= time period = 8 * 4 = 32 quarters

now, putting theses values in the above equation, we get,

FV = $18000 * (1 + 1.1225%)³²

FV = $18000 * (1 + 0.01125)³²

FV = $18000 * (1.01125)³²

FV = $18000 * 1.43045140243

FV = $25748.13

So, accumulated value is $25748.13.

(B) 4 % Compounded weekly:

Given: r = rate of interest = 4% converted weekly, so weekly rate = 4% / 52.14= 0.076716%,  n= time period = 8 * 52.14= 417.12 weeks

now, putting theses values in the above equation, we get,

FV = $18000 * (1 + 0.076716%)^417.12

FV = $18000 * (1 + 0.00076716)^417.12

FV = $18000 * (1.00076716)^417.12

FV = $18000 * 1.37695882356

FV = $24785.26

So, accumulated value is $24785.26.

(C) 2.8 % Compounded monthly:

Given: r = rate of interest = 2.8% converted monthly, so monthly rate = 2.8% / 12 = 0.2333%,  n= time period = 8 * 12 = 96 months

now, putting theses values in the above equation, we get,

FV = $18000 * (1 + 0.2333%)⁹⁶

FV = $18000 * (1 + 0.0023333)⁹⁶

FV = $18000 * (1.0023333)⁹⁶

FV = $18000 * 1.25074462315

FV = $22513.40

So, accumulated value is $22513.40.