Question

If $12,000 is invested at 2.5% for 20 years, find the future value if the interest is compounded the following ways. (Round your answers to the nearest cent.)

(a) annually
$  

(b) semiannually
$  

(c) quarterly
$  

(d) monthly
$  

(e) daily (N = 360)
$  

(f) every minute (N = 525,600)
$  

(g) continuously
$  

(h) simple (not compounded)
$

Answer 1

PV = $ 12000

Tenure (t) = 20 years

interest rate (i) = 2.5% p.a.

(a) If interest rate compounded annually,

Future value = PV x (1+i)^t = 12000 x (1+2.5%)²⁰ = $ 19,663.40

(b) If interest rate compounded semi-annually,

No of compounding in a year (N) = 2

Future value = PV x (1+i/N)^{t x N} = 12000 x (1+2.5% / 2 )^20x2 = $ 19,723.43

(c) If interest rate compounded quarterly,

No of compounding in a year (N) = 4

Future value = PV x (1+i/N)^{t x N} = 12000 x (1+2.5% / 4 )^20x4 = $ 19,753.89

(d) If interest rate compounded monthly,

No of compounding in a year (N) = 12

Future value = PV x (1+i/N)^{t x N} = 12000 x (1+2.5% / 12 )^20x12 = $ 19,774.37

(e) If interest rate compounded daily,

No of compounding in a year (N) = 360

Future value = PV x (1+i/N)^{t x N} = 12000 x (1+2.5% / 360)^20x360 = $ 19,784.31

(f) If interest rate compounded every minute,

No of compounding in a year (N) = 525,600

Future value = PV x (1+i/N)^{t x N} = 12000 x (1+2.5% / 525600 )^20x525600 = $ 19,784.66

(g) If interest rate compounded continuously,

No of compounding in a year (N) = 525,600

Future value = PV x e^ixt = 12000 x e^{0.025 x 20} = 12000 x 1.648721 = $ 19,784.66

(h) If interest rate is simple,

Future value = PV + PV x i x t = 12000 + 12000 x 2.5% x 20 = $ 18,000

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