A group of Psychology students at the University of Makati want to start a research project. They need P100,000 to fund their project. How much should they invest now in an account that earns \( 5 \% \) interest compounded annually to have the required amount in 3 years?

2) O montante (M) de determinado capital em um fundo de investimento, após o tempo (t) em anos, é dado pela fórmula \( M(t)=C \cdot 1,5^{\dagger} \). Nessas condiçōes, o tempo necessário para que um capital de R\$ 800 investido gere um montante de R\$ 4050 é de: a) 3 anos b) 4 anos c) 5 anos d) 6 anos e) 7 anos

Question 1 Mpho is a utility maximizing consumer. Her Cobb Douglas Utility function is given by \[ U(X, Y)=X^{\frac{1}{4}} Y^{\frac{3}{4}} \] (a) Derive the Marshallian demand curves for good \( X \) and \( Y \). (b) (i) Derive the indirect utility function (ii) Derive the expenditure function from (b) (i). (iii) Derive the Hicksian demand curve for good \( X \). (iv) Why are these demand curves termed compensated demand curves? (c) You are given that the price of \( X, P_{x} \) is R 15 , whilst the price of \( Y, P_{y} \) is R 45 . The consumer's budget M is fixed at \( \mathrm{R} 540(M=540) \). (i) Use the Marshallian demand curves from (a) to find the values of \( X \) and \( Y \). (ii) Compute and comment on Mpho's marginal rate of substitution.

\( \Rightarrow - 600000 + \frac { 102000 } { ( 1 + r ) ^ { 1 } } + \frac { 130000 } { ( 1 + r ) ^ { 2 } } + \frac { 161000 } { ( 1 + r ) ^ { 1 } } + \frac { 950000 } { ( 1 + r ) ^ { 4 } } + \frac { 950000 } { ( 1 + r ) ^ { 5 } } + \frac { 960000 } { ( 1 + r ) ^ { 6 } } = 0 \)

35) If the interest earned on a sum of money invested for 3 years at the annual interest rate of \( 10 \% \) compounded annually is \( ₹ 14,895 \), then what is the sum of money invested?

A group of Psychology students at the University of Makati want to start a research project. They need P100,000 to fund their project. How much should they invest now in an account that earns \( 5 \% \) interest compounded annually to have the required amount in 3 years?