Question

I. Find the present and future value of $1000 received every month end for 20 years if the interest rate is J12 = 12% p.a.

II. Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years.

III. John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

Answer 1

I.

$$j_{12}=12\%, n=20\ years, C=\$1000$$

$$FV=C\bigg({(1+j_{12}/12)^{12n}-1 \over j_{12}/12}\bigg)$$

$$FV=\$1000\bigg({(1+0.12/12)^{12(20)}-1 \over0.12/12}\bigg)=\$989255.37$$

$$PV=C\bigg({1-(1+j_{12}/12)^{-12n} \over j_{12}/12}\bigg)$$

$$PV=\$1000\bigg({1-(1+0.12/12)^{-12(20)} \over0.12/12}\bigg)=\$90819.42$$

II.

$$PV=C\bigg({1-(1+j_{1})^{-n} \over j_{1}}\bigg)(1+j_1)$$

$$PV=\$10000\bigg({1-(1+0.12)^{-10} \over 0.12}\bigg)(1+0.12)=\$63282.50$$

III.

$$A=P(1+j_{12})^n=\$10000(1+0.06)^{20}=\$32071.35$$

$$FV=C\bigg({(1+j_{12}/12)^{12n}-1 \over j_{12}/12}\bigg)$$

$$FV=\$X\bigg({(1+0.06/12)^{12(20)}-1 \over0.06/12}\bigg)=\$462.040952\cdot X$$

$$A+FV\geq\$2000(12)(15)$$

$$\$32071.35+\$462.040952\cdot X\geq \$360000$$

$$X\geq\$709.74$$