Question

13. Your father invested a lump sum 35 years ago at 6.75 percent interest compounded monthly. Today, he gave you the proceeds of that investment which totalled OMR 77,223. How much did your father originally invest?

Answer 1

Solution>

The formula for calculating the value of an Investment with compound Interest is

V = P * [ ( 1 + (r/n) ) ^ n * t ]

Where

V = Value of Investment i.e., amount of Investment today   ;

P = Principal Investment   ;   r = rate of interest   ;

n = No. of compounding periods per year ; t = Time in years

As per the information given in the question we have

V = $ 77,223 ;   r = 6.75 % = 0.0675 ; n = 12 ( Since compounding is monthly ) ;  

t = 35 Years ; P = $ To find    ;

Applying the above values in the formula we have

$ 77,223 = P * ( 1 + ( 0.0675 / 12 ) ) ^12 * 35

$ 77,223 = P * ( 1 + ( 0.0675 / 12 ) ) ^420

$ 77,223 = P * ( 1 + 0.005625 ) ^420

$ 77,223 = P * ( 1.005625) ^420

$ 77,223 = P * 10.5474

P = $ 77,223 / 10.5474

P = $ 7,321.513

P = $ 7,321.51 ( When rounded off to the nearest cent )

Thus the amount that was invested 35 years ago = $ 7,321.51

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