Calculate the value where you find question mark "?". All values should be determined up to four decimal places

Time value of money

        PV               r                       n                    FV             Interest amount                COMPOUND

A    50,000         10.50%          5 years            ?                   N/A                                   monthly

B     ?                     9%              15 years        2,500,000        N/A                                   quarterly 

C 140,000 ? 3 years 200,000 60,000 semi-annual

D 200,000 7.50% ? 400,000 200,000 quarterly

E ? 12% 10 years N/A 500,000 yearly

We know

FV = PV (1+r/t)^nt

where FV is future value

PV is present value

r is interest rate (in p.a)

t is number of times interest rate is to be compounded

n is time (in years)

Step-by-step explanation

Case A

n = 5 years

t= 12 (since compounding is monthly i.e. 12 times in year)

r = 10.50%

So,

FV = 50,000 x [1+(10.50%/12)]^5x12

FV = 50,000 x (1+0.0088)⁶⁰

FV = 84330.1491

Case B

n = 15 years

t= 4 (since compounding is quarterly)

r = 9%

So,

FV = PV x [1+(9%/4)]^15x4

FV = PV x (1+0.0225)⁶⁰

2,500,000/3.8001 = PV

PV = 657871.4022

Case C

n = 3 years

t= 2 (since compounding is semi annual)

r = r% (say)

So,

200,000 = 140,000 x [1+(r%/2)]^3x2

1.4286 = (1+(r%/2)⁶

On solving r = 12.2497%

Case D

n = n years (say)

t= 4 (since compounding is quarterly)

r = 7.50%

So,

400,000 = 200,000 x [1+(7.50%/4)]⁴ⁿ

2 = (1+0.0188)⁴ⁿ

2 = (1.0188)⁴ⁿ

On solving n = 9.3284 years

Case E

n = 10 years

t= 1 (since compounding is yearly)

r = 12%

Interest = 500,000

We know

PV + Interest = FV

PV + 500,000 = FV

So,

FV = PV x [1+(12%/1)]^10x1

FV = PV x (1.12)¹⁰

FV = 3.1058 PV

Substituting FV = PV + 500,000

We have,

PV + 500,000 = 3.1058 PV

2.1058 PV = 500,000

PV = 237,439.4529