Person X invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
Could someone provide solution to this problem ? Thanks.
let the total investment be 2P . R be the rate of interest. Time is 2years
Under SI, P will amount to P (1+ 2R/100)= P(1+ 0.02R) = P + 550- --eqn 1
eqn1 on simplifying becomes 0.02*P*R = 550 or 0.01*P*R =275
Under CI, P will amount to P (1+ R/100)^2 =P(1+ 0.01R)^2 = P + 605----eqn2
The SI for each year will be $275 (550/2) so compound interest in year 2 will be nothing but SI on amount $(P+275) at R rate of interest.
CI for 2years will be $275 + SI on (P+275) = 605
solving above we get P+275 is 330
Then (P+275)* 0.01R = 0.01*P*R + 2.75R = 330---eqn3 and we have 0.01*P*R =275 substituing this in equation3 we get 2.75R = 55
R = 20%
then 2P can be obtained as 2*0.01*P*20 = 275
2P = 2*27500/20 = $2750
Ans Option4. $2750