Question

1. What is G if B = A × (1+G)^T and B = 4,916, A = 2,111, and T = 11? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

2.What is A if P = [A/(1+R)^L] + [B/(1+R)^M] and P = 6,087, B = 1,499, R = 0.138, L = 4, and M = 9?  Round answer to nearest whole number.

3.What is A if P = [A × (1+R)^L] + [B × (1+R)^M] and P = 8,004, B = 1,591, R = 0.137, L = 4, and M = 10? Round answer to nearest whole number.

Answer 1

1.  B = A × (1+G)^T

B/ A= (1+G)^T

Taking logarithm (Base 10) on both sides, we get

log( B/ A) = log (1+G)^T

log( B/ A) = log (1+G)^T= T log (1+G)          [Using property  log mⁿ = n log m ]

Thus,  

Putting B=4916 ; A= 2111 , T= 11, we get log (1+G) =0.0333

or (1+G) = 10 ^0.0333 =1.079     [Using property  a^m = n if log_an = m ]

or G =1.079-1 = 0.079

2. P = [A/(1+R)^L] + [B/(1+R)^M]

[A/(1+R)^L]=P- [B/(1+R)^M]

Putting B= 1499 , R= 0.138 , M= 9 , P=6087

[A/(1+R)^L] = 6087- 468.29 =5618.7

or A= (1+R)^L​​​​​​​ X  5618.7 = 1.677 x 5618.7 = 9423.35 ~ 9423

3. P = [A × (1+R)^L] + [B × (1+R)^M]

[A × (1+R)^L]= P- [B × (1+R)^M]

Putting P= 8004 , B= 1591 , R= 0.137 , M= 10 , L = 4  , we get

= 1591 X 3.61 = 5744.799

= 1.671

Putting these values, we get

A= (8004-5744.799)/ 1.671

or A= 1351.8 ~ 1352